Question

8) An exterior angle of a triangle is 42° and the ratio of its opposite interior
angles is 2:5. Find the larger of the two interior angles.​

Answer 1

Answer:

The larger angle among the interior angles is 30°.

Step-by-step explanation:

We have,

An exterior angle of a Triangle = 42° and ratio of the two interior angles opposite to the exterior angles = 2 : 5

Now,

Let the Angles be 2x and 5x.

Remember, the larger of the two angles will be 5x, because 2 and 5 is being multiplied with x and since, 2 < 5, 5x will be greater than 2x.

Now, according to the theorem,

Sum of two interior angles is equal to its opposite exterior angle.

∴ 2x + 5x = 42°

7x = 42°

x = 42/7

x = 6

Now, we know that the larger angle of the two interior angles is 5x,

So,

5x = 5(6)

= 5 × 6

= 30°

Hence,

The larger angle among the interior angles is 30°.

Hope it helped and believing you understood it........All the best