In triangle ABC, angle B is 62 degrees, and angle A is 20 degrees less than angle C

In triangle ABC, angle B is 62 degrees, and angle A is 20 degrees less than angle C. Find the degree measure of angle A and determine the type of triangle ABC?

From the condition we know that in triangle ABC the angle B is equal to 62 °, and the angle A is 20 ° less than the angle C.

In order to find the degree measure of angle A and determine the type of triangle ABC, recall and apply the theorem on the sum of the angles of a triangle and compose and solve a linear equation.

Let’s denote by the variable x the degree measure of the angle C, then the angle A can be written as (x – 20).

The angles of a triangle add up to 180 °.

Let’s compose and solve the equation:

62 + x + x – 20 = 180;

2x = 180 + 20 – 62;

2x = 138;

x = 69 °.

Angle A is 69 – 20 = 49 °.

All angles of a triangle are acute – an acute-angled triangle.