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14.Among the two supplementary angles,the measure of the larger angle is 36° more than the measure of smaller.Find their measures.
15.My mother is 12 years more than twice my age.After 8 years,my mother's age will be 20 years less than three times my age.Find my age and my mother's age.
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Answer:
14. x - smaller angle
x + 36° - larger angle
supplementary angles are 2 angles with a total of 180°
x + (x + 36°) = 180°
2x + 36° = 180°
2x = 180° - 36°
2x = 144°
x = 72° --- smaller angle
x + 36°
72° + 36° = 108° --- larger angle
15. x - my age (present)
y - my mother's age (present)
y = 2x + 12
x + 8, my age (after 8 years)
y + 8, my mother's age (after 8 years)
y + 8 = 3(x + 8) - 20
2x + 12 + 8 = 3x + 24 - 20
2x + 20 = 3x + 4
20 - 4 = 3x - 2x
x = 16 ---- my age
y = 2x + 12
y = 2(16) + 12
y = 32 + 12
y = 44 --- my mother's age