Question

5. If mZWXZ = (5x + 3)", mZZXY = (8x - 4)", and

ZWXY is a right angle, find each measure.
W
Х
z
Y
mZWXZ =
mZZXY =

Answer 1

m∠WXZ = 38°

m∠ZXY = 52°

Explanation:

In the question

• ∠WXZ and ∠ZXY are two adjacent angles and formed together ∠WXY

• That means the measure of ∠WXY equal the sum of measures of ∠WXZ and ∠ZXY

∵ ∠WXY is a right angle

→ That means its measure is 90°

∴ m∠WXY = 90°

∵ m∠WXZ + m∠ZXY = m∠WXY

∵ m∠WXZ = (5x + 3)°

∵ m∠ZXY = (8x - 4)°

∵ m∠WXY = 90°

→ Substitute their values in the equation above

∴ (5x + 3) + (8x - 4) = 90

→ Add the like terms in the left side

∵ (5x + 8x) + (3 - 4) = 90

∴ 13x + (-1) = 90

∴ 13x - 1 = 90

→ Add 1 to both sides

∴ 13x - 1 + 1 = 90 + 1

∴ 13x = 91

→ Divide both sides by 13

∴
`(13x)/(13)=(91)/(13)`

∴ x = 7

→ To find the measure of each angle substitute x by 7 in their measures

∵ m∠WXZ = 5x + 3

∴ m∠WXZ = 5(7) + 3

∴ m∠WXZ = 35 + 3

∴ m∠WXZ = 38°

∵ m∠ZXY = 8x - 4

∴ m∠ZXY = 8(7) - 4

∴ m∠ZXY = 56 - 4

∴ m∠ZXY = 52°