Find the measure of the three angles in a triangle, if the measure of second angle is twice the first and the third angle is 20 degrees fewer than the first.
THANK YOU!
Angles are:
First angle:
A
Second angle B
Third angle C
The measure of second angle is twice the first means:
B = 2 A
The third angle is 20° fewer than the first means:
C = A - 20°
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 2 A + A - 20° = 180°
4 A - 20° = 180°
Add 20° to both sides
4 A = 200°
A = 200° / 4 = 50°
Now:
B = 2 A = 2 ∙ 50° = 100°
C = A - 20° = 50° - 20° = 30°
Three angles in this triangle are:
50° , 100° , 30°