Question

An exterior angle of a triangle is 103 degrees and two of its interior opposite angles are equal.find the angles

Answer 1

Question:

An exterior angle of a triangle is 103° and two of its interior opposite angles are equal. Find the angles of the triangle.

Answer:

51.5° , 51.5° , 51.5°

Note:

• A polygon of three sides is called triangle.

• A triangle has three angles.

• The sum of all the three interior angles is equal to 180°.

• An exterior angle of a triangle is equal to the sum of its two opposite interior angles.

Solution:

Let a ∆ABC such that angle A and angle B are equal (each equal to x) and angle C be y .

Also, let the exterior angle opposite to angle A and angle B be z .

{ Also, refer to the attachment }

Now,

In ∆ABC , we have;

=> angle A + angle B + angle C = 180°

=> x + x + y = 180°

=> 2x + y = 180° -------(1)

Also,

It is given that , the exterior angle opposite to A and B is equal to 103° .

=> z = 103°

=> angle A + angle B = 103°

=> x + x = 103°

=> 2x = 103°

=> x = 103°/2

=> x = 51.5°

Now,

Putting 2x = 103° in eq-(1) , we get;

=> 2x + y = 180°

=> 103° + y = 180°

=> y = 180° - 103°

=> y = 77°

Hence,

The angles of the given triangle are ;

51.5° , 51.5° , 77° .

Answer 2

please tell it in short way