Find the measure of the angle which is a complement of itself.

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30 °

90 °

45 °

180 °

answer is C.

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Detailed Solution

Given that the measure of the angle is a complement of itself.
Let the measure of an angle be

x °,

then the measure of its complement is also

x °

.
We know that,
The sum of the measures of an angle and it's complementary is

90 °

∴ x ° + x ° = 90 °

⇒ 2 x ° = 90 °

⇒ x ° = 90 ° 2 ⇒ x ° = 45 °

The measure of the angle which is complement of itself is

45 °

.
Hence, the correct option is 3.

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