An exterior angle of a triangle is 110° and its two interior opposite angles are equal. Each of these equal angles is
Question:
An exterior angle of a triangle is 110° and its two interior opposite angles are equal. Each of these equal angles is
(a) $70^{\circ}$
(b) $55^{\circ}$
(c) $35^{\circ}$
(d) $27 \frac{1^{\circ}}{2}$
Solution:
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).
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