What is the m∠ABC?

Solution:

According to the angle sum property of a triangle, the sum of all three interior angles of a triangle is 180 degrees. 

A triangle is a closed figure formed by three line segments, consisting of interior as well as exterior angles. 

The angle sum property is used to find the measure of an unknown interior angle when the values of the other two angles are known.

From the figure,

∠BAC = 75°

∠ACB + 135° = 180°

∠ACB = 180° - 135°

∠ACB = 45°

We know, sum of interior angles of triangle is equal to 180°

∠ABC + ∠BAC + ∠ACB = 180°

Substituting the values

∠ABC + 75° + 45° = 180°

∠ABC + 120° = 180°

So we get

∠ABC = 180° - 120°

∠ABC = 60°

Therefore, the m∠ABC is 60°.

What is the m∠ABC?

Summary:

The value of m∠ABC in the given figure is 60°.