# Expert Maths Tutoring in the UK

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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.

Therefore, the measure of an exterior angle of a triangle is equal to the sum of the measure of the two interior opposite angles.

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