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777dan777
3 months ago
8

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

Mathematics
2 answers:
lawyer [12.5K]3 months ago
6 0

We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.

Their measures are given as:

∠UVW = x - 10

∠XYZ = 4x - 10

Adding these, we have:

(x - 10) + (4x - 10) = 90

Simplifying:

5x - 20 = 90

Adding 20 to both sides:

5x = 110

Dividing by 5:

x = 22

Substituting back:

∠UVW = 22 - 10 = 12°

∠XYZ = 4(22) - 10 = 78°

Therefore, the values are:

x = 22°

∠UVW = 12°

∠XYZ = 78°

zzz [12.3K]3 months ago
3 0

Answer:

The angle measures are:

m∠UVW = 12°

m∠XYZ = 78°

Explanation:

Given that ∠UVW and ∠XYZ sum to 90°, and:

m∠UVW = (x - 10)°, m∠XYZ = (4x - 10)°

By definition of complementary angles:

(x - 10) + (4x - 10) = 90

This leads to:

5x - 20 = 90

Add 20 on both sides:

5x = 110

Divide both sides by 5:

x = 22°

Use x to find the angles:

m∠UVW = 22 - 10 = 12°

m∠XYZ = 4(22) - 10 = 78°

Hence, m∠UVW is 12°, and m∠XYZ is 78°.

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