Question

Compute the missing angles in the given figure.

Answer 1

x=52°

Explanation:

∠LNP+142°=180°

∠LNP=180°-142°

= 38°

∠LMN=x

x+90°+38°=180°

x+128°=180°

x=180°-128°

=52°

Answer 2

x = 52°

Explanation:

In the given figure,

142° is an exterior angle of triangle LMN

∠L = 90°

∠M = x

Exterior angle theorem: Sum of two opposite interior angle of a triangle is equal to exterior angle of triangle.

Therefore,

∠LMN + ∠MLN = ∠MNP

x + 90° = 142°

x = 142° - 90°

x = 52°

Hence, The missing angle is 52°