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If an angle is $30 °$ more than one half of its complement, then its measure is ____ °.

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Detailed Solution

If an angle is

30 °

more than one half of its complement, then its measure is 50°.
Given an angle is

30 °

more than one half of its complement.
An angle's complement and its sum are equal to 90°.
Use the attribute of an angle's complement and give the complement of the angle the value A.

(A 2 + 30 ∘) + A = 90 ∘ ⇒ A 2 + A = 90 ∘ − 30 ∘

⇒ 3 A 2 = 60 ∘

⇒ A = 60 ∘ × 23

⇒ A = 40 ∘

Now, the angle is,

⇒ (A 2 + 30 ∘) = 40 ∘ 2 + 30 ∘

⇒ (A 2 + 30 ∘) = 20 ∘ + 30 ∘

⇒ (A 2 + 30 ∘) = 50 ∘

Hence, the measure of angle is 50°.

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