The measure of an exterior angle of a triangle is equal to the sum of the measure of the two__?
A triangle is a 3 side polygon that has 3 interior angles. The angle that lies outside the triangle is called the exterior angle.
Answer: The measure of an exterior angle of a triangle is equal to the sum of the measure of the two interior opposite angles.
Let’s solve it by using the exterior angle theorem.
Explanation:
According to the exterior angle theorem, the measure of every exterior angle of a triangle is equal to the sum of the interior opposite angles.
Let's understand this using the diagram below,
From the given figure,
∠a + ∠b + ∠c = 180º [angle sum property of a triangle] -------------------- (1)
Also, ∠b + ∠d = 180º [Linear Pair] ---------------- (2)
Hence, ∠a + ∠b + ∠c = ∠b + ∠d [From (1) and (2)]
On solving we get,
∠a + ∠c = ∠d
Where,
∠d = exterior angle of triangle PRQ
∠a and ∠c are interior angles of triangle PRQ which are opposite to the external angle ∠d.
Hence, the measure of an exterior angle of a triangle is equal to the sum of the measure of the two interior opposite angles.