Find unknown angle measures of trapezoids

A trapezoid is a quadrilateral with exactly two sides parallel

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QUESTION OF
Views #: 33
Questions #: 10
Time: 10 minutes
Pass Score: 80.0%
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Angle Measures in an Isosceles Trapezoid

1 pts
volume_mute

Trapezoid ABCD is an isosceles trapezoid where the top base segment AB is parallel to the bottom base segment DC (\(AB \parallel DC\)). The non-parallel sides (legs) AD and BC are equal in length.

If the measure of interior angle D is \(70^\circ\), determine the measure of interior angle C.

DCAB70°?
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Finding a Consecutive Interior Angle

1 pts

In the trapezoid ABCD shown below, side AB is strictly parallel to side DC (\(AB \parallel DC\)). Given that the interior base angle D measures \(73^\circ\), calculate the exact degree measure of interior angle A.

DCAB73°x
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Interior Angles of a Right-Angled Trapezoid

1 pts
volume_mute

A trapezoid PQRS has parallel top and bottom bases PQ and SR. Side PS is perpendicular to both bases, creating internal right angles at vertices P and S. If the measure of angle R is discovered to be \(118^\circ\), find the degree measurement of angle Q.

PQRS118°?
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Sum of Interior Angles of a Quadrilateral

1 pts

In a structural scale model, a flat structural support bracket is shaped as a generic trapezoid. Three of its interior angles are accurately measured to be \(112^\circ\), \(68^\circ\), and \(135^\circ\). What must be the measure of the final, fourth interior angle?

Answer = (1)

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Explanation

Algebraic Side-Angle Properties

1 pts
volume_mute

In trapezoid ABCD, the top horizontal base side AB is parallel to the bottom horizontal base side DC (\(AB \parallel DC\)). The measures of the interior angles adjacent to leg AD are algebraically expressed as:
• \(m\angle A = (3x + 15)^\circ\)
• \(m\angle D = (2x - 10)^\circ\)

Solve the linear equation to discover the correct value of the variable \(x\).

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Explanation

Angle Measures in a Scalene Trapezoid

1 pts

For the non-isosceles (scalene) trapezoid drawn below, the top and bottom edge segments are parallel lines. Use angle relationships to solve for the missing values and match each unknown interior angle letter to its exact numerical degree measure.

62°48°xy

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

To delete a match, double click on a line

Angles

Angle x
Angle y

Measures

118°
132°
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Explanation

Identifying Supplementary Angle Pairs

1 pts

In a geometric trapezoid configuration where the horizontal top base segment UV is parallel to the bottom base segment XY, match the upper interior vertices to the placeholder blanks that correctly name their supplementary counterpart angle.

Angle U is supplementary to Angle (1).
Angle V is supplementary to Angle (2).

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Explanation

Classifying Angle Categories in Trapezoids

1 pts

Classify the following properties or descriptive pairs of interior angles for a flat Euclidean trapezoid whose horizontal upper side is parallel to its horizontal lower side.

drag and drop the selected option to the right place

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Explanation

Angle Relationships along a Transversal

1 pts
volume_mute

When calculating unknown missing interior angle measures inside a standard trapezoid, the rule stating that consecutive interior angles are supplementary relies fundamentally on the geometric concept that the two bases are parallel lines intersected by a leg line that acts as a transversal line.

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Key Geometrical Term Identification

1 pts
Click or touch the word(s) you want to choose
volume_mute

A closed, flat four-sided polygon (quadrilateral) that contains exactly one pair of parallel opposite boundary line segments is properly designated as a trapezoid.

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Explanation

✕
0
sin cos tan
sin-1 cos-1 tan-1 π e
xy x3 x2 ex 10x
y√x 3√x √x ln log
( ) 1/x % n!
7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC
Keywords
Year 9