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Two angles of a quadrilateral are of measure $65 °$ and the other two angles are equal. What is the measure of each of these two angles?

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115 °

105 °

120 °

135 °

answer is A.

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Detailed Solution

Given that the two angles of a quadrilateral are of measure

65 °

.
As we know that the sum of all angles of a quadrilateral is

360 °

Let the measure of two unknown angles be x ° and equating the sum all given angles with 360 ° . x ∘ + x ∘ + 65 ° + 65 ° = 360 ° ⇒ 2 x ° + 130 ° = 360 ° ⇒ x ° = 360 − 130 2 ° ⇒ x ∘ = 115 ∘

The value of each two angles is

115 °

.
Hence, the correct option is 1.

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