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Question

An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio 2:3. Find the angles of the triangle.


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Solution

Exterior Angle Theorem.

When one of the sides of a triangle is extended, the external angle formed between the extended side and its adjacent side is called an exterior angle.

The Exterior Angle Theorem states that “The exterior angle is equal to the sum of interior opposite angles of a triangle”.

Consider the ABC. Draw an exterior angle to the ABC by extending the side BC.

Given the exterior angle of a triangle is 110° and its interior opposite angles are in the ratio 2:3.

Therefore, ACD=110° and A:B=2:3.

Let A=2α and B=3α.

Hence, by the Exterior Angle Theorem,

ACD=A+B110°=2α+3α110°=5αα=110°5α=22°

Therefore,

A=2αA=2×22°A=44°

and

B=3αB=3×22°B=66°

Since the sum of all the angles of a triangle is equal to 180°, therefore
A+B+C=180°44°+66°+C=180°110°+C=180°C=180°-110°C=70°

Therefore, the angles of the triangle are 44°, 66° and 70°.


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