Question

5. In a triangle one of the exterior angle is 105°. One of the interior opposite angle is 75°.
Find the measure of all the angles of the triangle.​

Answer 1

Answer:

Step-by-step explanation:

Let another interior opposite angle be 'x'

We know,

105 =75+x (Exterior angle is equal to two interior opposite angle)

105-75=x

30=x

NOw,

Let the remaining angle of triangle be'y'

75+30+y=180   (Sum of angle of triangle is 180)

105+y=180

y=180-105

y=75

Answer 2

Answer:

The measures of all the angles of the triangle are:

75°, 30° and 75°.

Step-by-step explanation:

5. In a triangle, one of the exterior angle is 105°.

One of the interior opposite angle is 75°.

We know the, any exterior is equal to the sum of the pair of interior opposite angles.

Therefore, the other interior opposite angle = 105° - 75° = 30°

We also know that the sum of angles of any triangle is 180°.

Therefore, the measure of the remaining angle is 180° - 75° - 30° = 75°

Therefore, the measures of all the angles of the triangle are:

75°, 30° and 75°.