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An angle is equal to 8 times its complement. Determine its measure.
Given:
An angle is equal to 8 times its complement.
To do:
We have to find the measure of the angle.
Solution:
Two angles are said to be complementary if the sum of their measures is $90^o$.
Let the required angle be $x$.
This implies,
The measure of the complementary angle $=90^o-x$
According to the question,
$x=8(90^o-x)$
$x=720^o-8x$
$x+8x=720^o$
$9x=720^o$
$x=\frac{720^o}{9}$
$x=80^o$
The measure of the required angle is $80^o$.
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