The sum of two angles is 123° and their difference is 13°. Find all

1.	The sum of two angles is 123° and their difference is 13°. Find all the angles of the triangle.
Answer» Let two angles are x and y, then according to question ∠x + ∠y = 123° …(i) and ∠x – ∠y = 13° …(ii) Adding (i) and (ii), we get 2∠x = 136° ⇒ ∠x = 68° Now substituting ∠x = 68° in equation (i), we get 68° + ∠y = 123° ⇒ ∠y = 123° – 68° = 55° Third angle = 180° – 123° = 57° Hence angles of a triangle are 68°, 55°, 57°.

The sum of two angles is 123° and their difference is 13°. Find all the angles of the triangle.

Answer»

Let two angles are x and y, then according to question

∠x + ∠y = 123° …(i)

and ∠x – ∠y = 13° …(ii)

Adding (i) and (ii), we get

2∠x = 136° ⇒ ∠x = 68°

Now substituting ∠x = 68° in equation (i), we get

68° + ∠y = 123°

⇒ ∠y = 123° – 68° = 55°

Third angle = 180° – 123° = 57°

Hence angles of a triangle are 68°, 55°, 57°.