Question

If exterior angle of a triangle is 130 degree and one of the opposite interior angle is double of another, find all angle of triangle.​

Answer 1

ANSWER:

Given

• Exterior angle of a traingle = 130°
• One of the interior opposite angle is double the other

Let one of the interior opposite angle be ‘x’

Then the other opposite angle will be = 2x

★ Using property:

Opposite angle = sum of two interior opposite angles

Interior opposite angles = x° , 2x°

➳ x° + 2x° = 130°

➳ 3x° = 130°

➳ x° = 43.3°

♦ Other angle = 2x° = 2(43.3) = 86.6°

★ Using property

Sum of all angles in a triangle = 180°

→ This property is also known as angle sum property

Let the other angle be y°

➻ x° + 2x° + y° = 180°

➻ 43.3° + 86.6° + y° = 180°

➻ 129.9° + y° = 180°

➻ y° = 180° - 129.9°

➻ y° = 51.1°

Hence, angles of triangle are 43.3° , 86.6° , 51.1°

Answer 2

Answer:

• Exterior angle = 130°
• One of the interior opposite angles is double of the another interior opposite angle .

The theorem that will be used here will be - The sum of interior opposite angles is equal to the exterior angle.

So, let us assume that one of the angles that is interior opposite to the exterior angle is x and the other one is 2x.

Hence, according to the question,

➸ 2x° + x° = 130°

Solving it find the value of x°.

➸ 3x° = 130°

➸ x° = 130/3

➸ x° = 43.33°

Hence, one of the angle interior opposite to the exterior angle = x° = 43.33°

The other interior opposite angle which is double of the x° = 2x° = 2*43.33 = 86.66°

Now, we got two angles of the triangle.

By, angle sum property we can get the third angle of the triangle.

Let the unknown angle be z°.

➸ 86.66 + 43.33 + z° = 180°

➸ 129.99 + z° = 180°

➸ z° = 180 - 129.99

➸ z° = 50.01°

Hence, the third angle of the triangle = 50.01°.