Two angles of a quadrilateral are of measure 65° and the other two angles are equal.
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 $115^{\circ}$