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?
Solution:
Let $x$ be the measure of each angle.
Since, the sum of all the angles of a quadrilateral is $360^{\circ}$, we have:
$65^{\circ}+65^{\circ}+x^{\circ}+x^{\circ}=360^{\circ}$
$\Rightarrow 2 x^{\circ}+130^{\circ}=360^{\circ}$
$\Rightarrow 2 x^{\circ}=230^{\circ}$
$\Rightarrow x^{\circ}=115^{\circ}$
$\therefore$ The measure of each angle is $115^{\circ}$