Question

An exterior angle of a triangle is ${110}^{\circ }$ and its two interior opposite angles are equal. Each of these equal angles is

$\left(a\right){70}^{\circ }$

$\left(b\right){55}^{\circ }$

$\left(c\right){35}^{\circ }$

$\left(d\right)27{\frac{1}{2}}^{\circ }$

Answer 1

ANSWER:
Let the measure of each of the two equal interior opposite angles of the triangle be x.
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles.
∴ x + x = 110°
⇒ 2x = 110°
⇒ x = 55°
Thus, the measure of each of these equal angles is 55°.
Hence, the correct answer is option (b).