The sum of the angles of any four-sided figure (called a quadrilateral ) is $360 ^ { \circ }$ . The quadrilateral shown has two equal base angles. Find x.
A) $x = 54 ^ { \circ }$
B) $x = 61 ^ { \circ }$
C) $x = 58 ^ { \circ }$
D) $x = 59 ^ { \circ }$
E) $x = 56 ^ { \circ }$

Question

The sum of the angles of any four-sided figure (called a quadrilateral ) is $360 ^ { \circ }$ . The quadrilateral shown has two equal base angles. Find x. 
A) $x = 54 ^ { \circ }$ 
B) $x = 61 ^ { \circ }$ 
C) $x = 58 ^ { \circ }$ 
D) $x = 59 ^ { \circ }$ 
E) $x = 56 ^ { \circ }$

Quizplus · Accepted Answer

Let the base angles each have a measure of $y$. Since the sum of the angles in a quadrilateral is $360^\circ$, we have $y+y+90^\circ+x+180^\circ=360^\circ$, which simplifies to $2y+x=90^\circ$. We also know that the sum of the angles in a triangle is $180^\circ$, so the third angle in the triangle with base angles $y$ must be $180^\circ-2y$. Therefore, the sum of all angles in the quadrilateral is $90^\circ+(180^\circ-2y)+(2y)+x+90^\circ=360^\circ$, which simplifies to $180^\circ+x=360^\circ$, so $x=\boxed{	extbf{(C) }58^\circ}$.

The Sum of the Angles of Any Four-Sided Figure (Called 360∘360 ^ { \circ }360∘

The Sum of the Angles of Any Four-Sided Figure (Called $360 ^ { \circ }$