Question

The measures of the angles in △ABC are given by the expressions in the table.

Angle Measure
A 65°
B (3x−10)°
C (2x)°
Find the value of x. Then find the measures of angles B and C.



Enter your answers in the boxes.
x =

m∠B=
º

m∠C= ​
º

Answer 1

the summation of angles of a triangle is 180°. measure angles of B and C by,
m∠A + m∠B + m∠C=180°
65° + (3x−10)° + (2x)°=180°
5x=180°- 65°+ 10°
x=125/5, x=25
B=(3x−10)°=3(25)-10=65
C=2x=2(25)=50

Answer 2

We know that the summation of angles of a triangle is 180°. Then we can measure angles of B and C by,
m∠A + m∠B + m∠C=180°
65° + (3x−10)° + (2x)°=180°
Solve for variable x by transposing and combing same terms,
5x=180°- 65°+ 10°
x=125/5, x=25
Since we already know the value of x, we can proceed in solving B and C
B=(3x−10)°=3(25)-10=65
C=2x=2(25)=50
Therefore, the answers are x=25, B=65 and C=50.