Question

Find the measure of each angel

1. the measure of an angel is 1/4 the measure of its complement.

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A. thought provoking
sketch an intersection of road. identify any supplementary, complementary of vertical angles.

Answer 1

1.

We will write and solve an equation that expresses the given relation. Let x represent the angle measure. Its complement is (90-x).

... x =(1/4)(90 -x)

Subtract x and simplify

... 0 = (90/4) - (5/4)x

Divide by the coefficient of x, which is -5/4.

... 0 = -18 +x

Add the opposite of the constant.

... 18 = x

The angle is 18°.

2.

The attachment shows the intersction of road AB with road CD.

Supplementary angles: ∠CXA and ∠CXB; ∠BXC and ∠BXD; ∠DXA and ∠DXB; ∠AXC and ∠AXD.

Complementary angles: none

Vertical angles: ∠AXC and ∠BXD; ∠BXC and ∠AXD.