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Question

# The measure of an angle is 52 more than the measure of its complement. What is the measure of the angle?

Solution

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Let $x$ be the angle so that its complement is $90-x$, both in degrees.

The measure of the angle is 52 more than the measure of its complement so we can write:

$x=(90-x)+52$

Solving for $x$,

$x=142-x$

$2x=142$

$x=71$

So, the measure of the angle is $\color{#c34632}71\text{\textdegree}.$

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