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Quizzes > Mathematics

Right Angles in a Trapezoid: How Many Can There Be?

Quick, free geometry quiz with instant results. See if a trapezoid with two right angles is possible.

Editorial: Review CompletedCreated By: Stephen ReganUpdated Aug 25, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art trapezoid with angle markers on sky blue background for quiz on how many right angles a trapezoid can have

This quiz helps you figure out how many right angles in a trapezoid are possible and spot them in clear drawings. Build skills with our angle relationships quiz, compare shapes in a trapezoid vs parallelogram quiz, or check fundamentals with a quick right angle test.

What is a right trapezoid?
A trapezoid with four right angles.
A trapezoid with two right angles.
A trapezoid with three right angles.
A trapezoid with at least one right angle.
A right trapezoid is defined by having one leg perpendicular to the base, which creates two right angles at either end of the leg. It is not merely one right angle, nor can it have three without becoming a rectangle. The distinctive feature is the perpendicular leg forming two right angles.
What is the maximum number of right angles a non-parallelogram trapezoid can have?
Two
One
Three
Four
A non-parallelogram trapezoid can have at most two right angles, both occurring where a leg meets a base. Having more would force both pairs of opposite sides to be parallel, turning it into a parallelogram. Thus two is the maximum for a trapezoid by definition.
In any quadrilateral, the sum of interior angles equals how many degrees?
90°
360°
540°
180°
The formula for the sum of interior angles in an n-sided polygon is (n - 2)×180°. For a quadrilateral, n=4, so (4 - 2)×180°=360°. This holds true for all quadrilaterals, including trapezoids.
Can a non-parallelogram trapezoid ever have four right angles?
Only if it's isosceles.
Yes, always.
Only if both legs are parallel.
No.
If a quadrilateral has four right angles, both pairs of opposite sides are parallel, making it a parallelogram. A non-parallelogram trapezoid has exactly one pair of parallel sides, so it cannot have four right angles. That configuration is a rectangle, not a trapezoid.
If a trapezoid has two right angles and the other two angles are x and y, what is x + y?
90°
180°
270°
360°
The sum of all interior angles in a quadrilateral is 360°. Two right angles total 180°, so the remaining two angles must also sum to 180° to reach 360°. This applies to any trapezoid or quadrilateral.
In coordinate geometry, given the trapezoid with vertices A(0,0), B(4,0), C(1,3), D(0,3), how many right angles does it have?
Two
Zero
Three
One
AB is horizontal and AD is vertical, so angle A is 90°. CD is horizontal and AD is vertical, so angle D is also 90°. The other angles are not right angles. Thus, the trapezoid has exactly two right angles.
In a cyclic trapezoid (one inscribed in a circle), if one angle is right, how many right angles must it have?
Three
Two
One
Four
Opposite angles in a cyclic quadrilateral sum to 180°. If one angle is 90°, its opposite must also be 90°. Therefore, a cyclic trapezoid with one right angle automatically has two right angles.
Which property guarantees that a trapezoid is a right trapezoid?
Legs of equal length.
Base angles are equal.
One leg perpendicular to a base.
Diagonals of equal length.
A right trapezoid is defined by having one leg perpendicular to the base, forming two right angles at that leg's endpoints. Equal diagonals define an isosceles trapezoid, and equal legs or base angles describe other special cases. Only perpendicularity of a leg ensures right angles.
Why is it impossible for a trapezoid to have exactly three right angles?
Diagonal lengths would contradict the Pythagorean theorem.
The legs must be equal if there are three right angles.
Three right angles sum to 270°, leaving 90° for the fourth, making it four.
Opposite sides would both be parallel then.
Three right angles total 270°. Since the interior angles of any quadrilateral sum to 360°, the fourth angle must be 90° as well. That yields four right angles, not three. Hence exactly three right angles is impossible.
If a trapezoid's two adjacent sides to the longer base satisfy the Pythagorean theorem relative to that base, how many right angles are formed at those vertices?
One
Four
Zero
Two
When each adjacent side to the base is perpendicular, each forms a right angle with that base. Two perpendicular legs produce two right angles at their intersections with the longer base. Other angles are not necessarily right.
If both legs of a trapezoid are perpendicular to its two parallel bases, what quadrilateral does it become?
Rectangle
Right trapezoid
Isosceles trapezoid
Parallelogram
When both legs are perpendicular to the parallel bases, all four angles are right angles and both pairs of opposite sides are parallel. This is the definition of a rectangle. Under the inclusive trapezoid definition, it is also a trapezoid.
Under which definition of trapezoid can a trapezoid have four right angles?
Right definition (legs perpendicular to bases)
Exclusive definition (exactly one pair of parallel sides)
Isosceles definition (legs of equal length)
Inclusive definition (at least one pair of parallel sides)
The exclusive definition excludes parallelograms, so a trapezoid cannot have four right angles under that rule. The inclusive definition counts parallelograms (including rectangles) as trapezoids, allowing four right angles. Other definitions focus on leg equality or perpendicularity but do not permit all four right angles.
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Study Outcomes

  1. Understand Trapezoid Angle Properties -

    Grasp the definition and key properties of trapezoid angles, including how many right angles a trapezoid can have.

  2. Identify Maximum Right Angles -

    Determine the upper limit on the number of right angles in various trapezoid types and distinguish between possible and impossible configurations.

  3. Calculate Angle Measures -

    Apply geometric rules to compute individual and complementary angles, reinforcing your understanding of degrees in trapezoid shapes.

  4. Analyze Trapezoid Variations -

    Compare isosceles, right, and general trapezoids to see how their angle measures and counts differ.

  5. Apply Knowledge in Quiz Scenarios -

    Solve interactive quiz questions to test your skills on how many right angles does trapezoid have and related angle problems.

  6. Interpret Sum of Interior Angles -

    Use the formula for the sum of interior angles in a quadrilateral to validate your answers about degrees of a trapezoid.

Cheat Sheet

  1. Trapezoid Fundamentals -

    Every trapezoid has exactly one pair of parallel sides, making it unique among quadrilaterals. Remember, the sum of all interior angles in any trapezoid is 360°, so understanding degrees in trapezoid shapes is key for angle calculations. (Source: University of Cambridge)

  2. Maximum Right Angles -

    Wondering how many right angles can a trapezoid have? At most two, since having a third right angle would force all sides to be perpendicular and ruin the parallel-side definition. This fact helps you instantly recognize right trapezoids during quizzes! (Source: Khan Academy)

  3. Supplementary Angle Strategy -

    Because one pair of opposite sides is parallel, any two adjacent angles between those sides sum to 180°. For example, if one base angle measures 70°, its neighbor is 110° (180°−70°). This trick is a lifesaver when filling in missing degrees of a trapezoid under time pressure. (Source: MIT OpenCourseWare)

  4. Isosceles Trapezoid Angle Rules -

    In an isosceles trapezoid, the non-parallel legs are congruent, which makes each pair of base angles equal - another degrees-of-a-trapezoid gem. If the lower left angle is 65°, the lower right is also 65°, and each top angle is 115° (360°−2×65°). (Source: Stanford University)

  5. Mnemonic for Angle Sums -

    Use the phrase "Parallel Lines Produce Supplements" (P.L.P.S) to recall that interior angles on the same side of a transversal add up to 180°. This mnemonic will keep "how many right angles does trapezoid have" facts and supplementary relationships fresh in your mind. (Source: National Council of Teachers of Mathematics)

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