Solving Angle Measures in Rug Design Using Vertical and Supplementary Angle Properties

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In this exercise, we analyze a rug design using angle measures with m1 = 122. Given that angles 1 and 3 are vertical angles, they share equal measures, so m3 equals 122. To solve for other angles, we use the relationships of supplementary angles and vertical angles. Through step-by-step calculations, we determine m2 = 58, and supplementary angles yield m6 = m8 = 43 and m5 = m7 = 137. Guided practice further explores angle measures to reinforce understanding of angle relationships.

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May 03, 2026

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Solving Angle Measures in Rug Design Using Vertical and Supplementary Angle Properties

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Find the angle measures indicated in the rug design if m1 = 122. It is given that m1 = 122. 1 and 3 are vertical angles.Their measures are equal, so m3 = 122. EXAMPLE 2 Solve a Multi-Step Problem Textiles SOLUTION STEP 1
180 m 1+m 2 = 122 + m 2 = 180 Substitute 122 form1. m 2 = 58 Subtract 122 from each side. 2 and 4 are vertical angles. Their measures are equal, so m4 . = 58 ANSWER m 1= m3 = 122, m 2 = m 4 = 58 EXAMPLE 2 Solve a Multi-Step Problem STEP 2 1 and 2 are supplementary. Definition of supplementary angles STEP 3
7. ANSWER m 6= m8 = 43, m 5 = m 7 = 137 . for Example 2 GUIDED PRACTICE Find the measures of the numbered angles.
8. ANSWER m 9 = m11 = 126 andm 8 = m 10 = 54 . for Example 2 GUIDED PRACTICE Find the measures of the numbered angles.