Question

∠UVW and ∠XYZ are complementary angles, m∠UVW=(x−10)º , and m∠XYZ=(4x−10)º .

Answer 1

we know that

if ∠UVW and ∠XYZ are complementary angles

then

∠UVW + ∠XYZ=90°

∠UVW=x-10

∠XYZ=4x-10

substitute the values

(x-10)°+(4x-10)°=90°

Solve for x

5x-20=90

5x=90+20

5x=110

x=22°

∠UVW=x-10=22-10=12°

∠XYZ=4x-10=4*22-10=78°

therefore

the answer is

x=22°

∠UVW=12°

∠XYZ=78°

Answer 2

Using the concept of complementary angles, it is found that:

• The measure of angle UVW is 12º.
• The measure of angle XYZ is 78º.

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• If two angles are complementary, the sum of their measures is 90º.

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• The measure of angle UVW is (x - 10)º.
• The measure of angle XYZ is (4x - 10)º.
• They are complementary, thus:

$x - 10 + 4x - 10 = 90$

$5x - 20 = 90$

$5x = 110$

$x = \frac{110}{5}$

$x = 22$

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$x - 10 = 22 - 10 = 12$

$4x - 10 = 4(22) - 10 = 88 - 10 = 78$

The measure of angle UVW is 12º.

The measure of angle XYZ is 78º.

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