Question

The exterior angles obtained on producing the base of a triangle both ways are 100° and 120°. Find all the angles

Answer 1

ANSWER:-

Given:

The exterior angles obtained on producing the base of a ∆ boths way are 100° & 120°.

To find:

Find all the angles.

Solution:

Let, ABC be a triangle & base BC produced to both sides. Exterior angles are ∠ABD & ∠ACE.

Therefore,

⏺️∠ABD = 100°

⏺️∠ACE = 120°

We know that, linear pair of ∆;

=) ∠ABD + ∠ABC = 180°

=) ∠ABC = 180° - ∠ABD

=) ∠ABC = 180° - 100°

=) ∠ABC = 80°

&

∠ACE + ∠ACB = 180° [Linear pair]

=) 120° + ∠ACB= 180°

=) ∠ACB= 180° -120°

=) ∠ACB= 60°

So,

In ∆ABC,

∠A + ∠B+ ∠C= 180°

=) ∠A + 80° + 60° = 180°

=) ∠A + 140° = 180°

=) ∠A = 180° -140°

=) ∠A= 40°

Thus,

angles of ∆ are 40°, 80° & 60°.

Hope it helps ☺️

Answer 2

Answer:

fffkgfrzyducysur Ystsudr yeud