Question

If two angles of a quadrilateral are of measure 75${}^{\circ }$ and the other two angles are equal, then the measure of the angle is

• A. 110${}^{\circ }$
• B. 105${}^{\circ }$
• C. 130${}^{\circ }$
• D. 120${}^{\circ }$

Answer 1

The correct option is B 105${}^{\circ }$

Let x be the measure of equal angles.
The sum of all the angles of a quadrilateral is 360${}^{\circ }$.

So,
$\Rightarrow$ 75${}^{\circ }$ + 75${}^{\circ }$ + x${}^{\circ }$ + x${}^{\circ }$ = 360${}^{\circ }$
$\Rightarrow$ 2x${}^{\circ }$ + 150${}^{\circ }$ = 360${}^{\circ }$
$\Rightarrow$ 2x${}^{\circ }$ = 210${}^{\circ }$
$\Rightarrow$ x${}^{\circ }$ = 105${}^{\circ }$
$\therefore$ The measure of the angle is 105${}^{\circ }$.