Question

In triangle ABC, the measures of angle B is three more than twice the measure of angle A, and the measure of angle C is two more than four times the measure of angle A. How can I find the measure of the angle in a triangle?

Answer 1

`hatA=25^@,hatB=53^@.hatC=102^2`

Explanation:

The sum of the 3 angles in the triangle`hatA+hatB+hatC=180^@`

In terms of angle A , angles B and C may be expressed as

`hatB=2hatA+3" and " hatC=4hatA+2`

`rArrhatA+2hatA+3+4hatA+2=180^@`

`rArr7hatA+5=180rArr7hatA=180-5=175`

divide both sides by 7

`(cancel(7)^1hatA)/cancel(7)^1=cancel(175)^(25)/cancel(7)^1rArrhatA=25`

Thus `hatA=25^@,hatB=(2xx25)+3=53^@`

and `hatC=(4xx25)+2=102^@`

Check: `25^@+53^@+102^@=180^@`