M∠WYX = (4x − 8)° and m∠WYZ = 10x°. If ∠WYX and ∠WYZ are complementary, find the measure of each angle.

Question

asked Jan 1, 2018 124k views

2 Answers

Running Rabbit · Answer 1 · 2018-01-05T21:29:53+0000

Answer:

$m\angle WYX=20^(\circ)$

$m\angle WYZ=70^(\circ)$

Explanation:

We have been given that
$m\angle WYX=(4x-8)^(\circ)$ and
$m\angle WYZ=(10x)^(\circ)$ .

Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.

$m\angle WYZ+m\angle WYX=90^(\circ)$

Substitute the given values:

4x-8+10x=90

Combine like terms:

14x-8=90

14x-8+8=90+8

14x=98

(14x)/(14)=(98)/(14)

x=7

Let us substitute
x=7 in measure of each angle as:

$m\angle WYX=(4(7)-8)^(\circ)$

$m\angle WYX=(28-8)^(\circ)$

$m\angle WYX=20^(\circ)$

Therefore, the measure of angle WYX is 20 degrees.

$m\angle WYZ=(10x)^(\circ)$

$m\angle WYZ=(10(7))^(\circ)$

$m\angle WYZ=70^(\circ)$

Therefore, the measure of angle WYZ is 70 degrees.