Question

An exterior angle of a triangle measures 120° And its interior opposite angles are in the ratio 5:7. Find the angles of the triangle.

Answer 1

Given,

The exterior angle of the triangle = 120°

The ratio of interior opposite angles = 5:7

To Find,

The angles of the triangle.

Solution,

By using the exterior angle property we get

5x +7x = 120

12x = 120

x= 10

So, the two angles will be 50 and 70

Now, we can find the third angle using the angle sum property

50 + 70 + c = 180

c = 60

Hence, the angles of the triangle are 50, 60, and 70.

Answer 2

Given: The exterior angle of the triangle = 120° and we have the ratio of interior opposite angles = 5:7

To Find: Here we have to find the angles of the triangle.

Solution:

we will use the exterior angle property we get

$5x +7x = 120 \\12x = 120\\x= 10$

So, the two angles will be 50 and 70

Now, we know that sum of angle is 180

So,

$50 + 70 + c = 180\\c = 60$

Final answer:

Hence, the angles of the triangle are 50, 60, and 70.