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Question
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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Solution
\[ \text{ Let x be the measure of each angle } . \]
\[\text{ Since, the sum of all the angles of a quadrilateral is } 360 °, \text{ we have: } \]
\[65° + 65° + x° + x° = 360° \]
\[ \Rightarrow 2x° + 130°= 360° \]
\[ \Rightarrow 2x° = 230° \]
\[ \Rightarrow x° = 115°\]
\[ \therefore \text{ The measure of each angle is } 115° .\]
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