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Chapter 12: Q10. (page 689)

Use the diagram shown. Identify all pairs of the specified angles.

Supplementary angles

Short Answer

Expert verified

In the quadrilateral, 鈭�A,鈭�Cand鈭�B,鈭�D form two supplementary angle pairs.

Step by step solution

01

Step 1. Given Information.

The figure is shown below.

02

Step 2. Concept used.

If the sum of two angles is 90掳 then the angles are called complementary angles and if the sum is 180掳 then the angles are called supplementary angles.

03

Step 3. Calculation.

The sum of measures of all the possible pairs of angles in the quadrilateral is,

鈭�A+鈭�B=170掳鈭�A+鈭�C=180掳鈭�A+鈭�D=90掳鈭�B+鈭�C=270掳

And,

鈭�B+鈭�D=180掳鈭�C+鈭�D=190掳

In the above list, only the pairs 鈭�A,鈭�C and 鈭�B,鈭�Dhave the sum of their measures equal to 180掳.

04

Step 4. Conclusion.

The pairs of supplementary angles in the quadrilateral are 鈭�A,鈭�C and 鈭�B,鈭�D.

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Most popular questions from this chapter

Use a compass and a straightedge to draw a segment whose length is the sum of the lengths of the given segments.

Use the given information to find m鈭�2.

鈭�1 and 鈭�2arevertical angles, and m鈭�1=140掳.

What can you say about the measures of two vertical angles?

Solve the equation by first clearing the fractions.

12x+34=56

Solve the equation. Check your solution.

10-3x=37
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