Question

The exterior angle obtained on producing the base of a triangle both ways or hundred degree and 120° . find all the angles. You can also write the answer in a sheet of paper and send the picture . that’s enough

Answer 1

Explanation:

Let the triangle be ABC and BC be extended to DE, such that

ABD = 100°, and ∠ACE = 120°.

Angles ABD and ACE form a linear pair. Hence,

$\mathsf{ABD + ABC=180}$

$\mathsf{==>100+ABC=180}$

$\mathsf{==> ABC = 180-100}$

∴ ∠ABC = 80°

Similarly, ∠ACE and ∠ACB form a linear pair, and so,

$\mathsf{ACE+ACB=180}$

$\mathsf{==>120+ACB=180}$

$\mathsf{==> ACB=180-120}$

∴ ∠ACB = 60°

By the angle sum property of a triangle, we know that

$\mathsf{ABC + ACB + BAC=180}$

$\mathsf{==> 80+60+BAC=180}$

$\mathsf{==>BAC=180-140}$

∴ ∠BAC = 40°

Hence, the angles of the triangle are 40°, 60° and 80°.

Answer: 40°, 60°, 80°

I hope this helps. :D