Question

The sum of two opposite angles of a quadrilateral is $172°$. The other two angles of the quadrilateral are equal. Find the equal angles.

Answer 1

Solution:

Given the sum of two opposite angles of a quadrilateral $=172°$.

Let $x$ be the measurement of equal angle.

We know the sum of all the angles of a quadrilateral is $360°$.

So,

$x+x+172=360$

$\Rightarrow 2x=360–172$

$\Rightarrow 2x=188$

$\Rightarrow x=\frac{188}{2}$

$\Rightarrow x=94$

Therefore the equal angles are $94°$ each.

Hence, the equal angles are $94°$,$94°$.