Question

2) Angle B of a triangle is 25 more than twice the measure of Angle A. Angle C is 15º morethan half the measure of Angle A. Find the measure of Angle B.

Answer 1

Let's set x for angle A.

Now, Angle B of a triangle is 25 more than twice the measure of Angle A. Then, we can write the next equation for angle B.

B = 25 + 2x

For angle C, " Angle C is 15º more than half the measure of Angle A". Then, w can write the next equation:

C = 15 + x/2

The measures of interior angles of a triangle add up to 180 degrees. Therefore:

A + B +C = 180

Replacing each equation:

x + 25 + 2x + 15+x/2 = 180

Solve for x:

3x + x/2+ 40 = 180

(7/2)x + 40 = 180

(7/2)x = 180-40

(7/2)x = 140

7x = 280

x = 280/7

x= 40

Then, angle A is equal to 40 degrees.

For angle B :

B = 25 + 2x

B = 25 + 2(40)

B = 105

Hence, the angle B is equal to 105 degrees.

For angle C

C = 15 + x/2

C = 15 + 40/2

C = 15 + 20

C = 35