Question

One of the exterior angles of a triangle is 1300 and the interior opposite angles are in the ratio 6:7. Find the measure of all the interior angles of the triangle. State the properties used

Answer 1

Answer:

Step-by-step explanation:

Let the two angles of the triangle be 6x and 7x.

Exterior angles of triangles = Interior angles of a triangle

1300° = 6x + 7x

1300° = 13x

x = 1300/13

x = 100

Answer 2

Given :  One of the exterior angles of a triangle is 130° and the opposite interior opposite angles are in the ratio 6:7.

To Find :  the measure of all the interior angles of the triangle.  

Solution:

Exterior angle of a triangle = sum of opposite interior angles

Sum of angles of a triangle is 180°  

or Linear Pair is 180°

Exterior angle = 130°

interior opposite angles are in the ratio 6:7.

Let say 6x and 7x

6x + 7x = 130°

=> 13x = 130°

=> x  = 10°

6x = 6 * 10° = 60°

7x = 7 * 10° = 70°

Sum of angles of a triangle = 180°

=> third angle = 180° - 60° - 70°  = 50°

or Linear pair = 180°

Hence 3rd interior angle = 180° - 130° = 50°

Hence interior angles of triangle are

50° , 60° and 70°

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