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If an angle measure $10^{o}$ more than its complement, then what is the measure of the angle?

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40^{o}

55^{o}

35^{o}

50^{o}

answer is D.

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Detailed Solution

It is given that an angle is 10° more than its complementary angles.
We know that the sum of two complementary angles is 90°.
Let

x

be an angle whose complementary angle is

(90 ° - x) .

According to the given condition,

x - (90 ° - x) = 10

⟹

x - 90 ° + x = 10

⟹

2 x = 100

\Rightarrow x = \frac{100 °}{2}

⟹

x = 50 °

.
So, the angle which is

10^{0}

more than its complement is

50^{0}

.
Hence, the correct option is 4.

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