(Note: In number 1, angles are vertical. Vertical angles are congruent. In number 2, angles are supplementary, their angle sum is 180°. In number 3, angles are complementary, their angle sum is 90°.)
1. 5x - 8 = 2x + 19
5x - 2x = 19 + 8
3x = 27
x = 9
m<ABC = 5x - 8
= 5(9) - 8
= 45 - 8
m<ABC = 37°
m<DBE = 2x + 19
= 2(9) + 19
= 18 + 19
m<DBE = 37°
2. 9x + 12 + 6x + 18 = 180°
15x + 30 = 180°
15x = 180 - 30°
15x = 150
x = 10°
m<ABD = 9x + 12
= 9(10) + 12
= 90 + 12
m<ABD = 102°
m<CBD = 6x + 18
= 6(10) + 18
= 60 + 18
m<CBD = 78°
3. 3x + 2x = 90°
5x = 90°
x = 18°
m<EBC = 2x = 2(18°) = 36°
m<DBE = 3x = 3(18) = 54°
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Answers & Comments
(Note: In number 1, angles are vertical. Vertical angles are congruent. In number 2, angles are supplementary, their angle sum is 180°. In number 3, angles are complementary, their angle sum is 90°.)
1. 5x - 8 = 2x + 19
5x - 2x = 19 + 8
3x = 27
x = 9
m<ABC = 5x - 8
= 5(9) - 8
= 45 - 8
m<ABC = 37°
m<DBE = 2x + 19
= 2(9) + 19
= 18 + 19
m<DBE = 37°
2. 9x + 12 + 6x + 18 = 180°
15x + 30 = 180°
15x = 180 - 30°
15x = 150
x = 10°
m<ABD = 9x + 12
= 9(10) + 12
= 90 + 12
m<ABD = 102°
m<CBD = 6x + 18
= 6(10) + 18
= 60 + 18
m<CBD = 78°
3. 3x + 2x = 90°
5x = 90°
x = 18°
m<EBC = 2x = 2(18°) = 36°
m<DBE = 3x = 3(18) = 54°