Question

the measures of the angles in $\triangle abc$ are given by the expressions in the table.

angle | measure
--- | ---
a | $65^circ$
b | $(3x - 10)^circ$
c | $(2x)^circ$

find the value of x. then find the $m\angle b$ and $m\angle c$.

enter your answers in the boxes.

$x = \square$

Explanation:

Step1: Sum angles to 180°

$65 + (3x - 10) + 2x = 180$

Step2: Simplify left-hand side

$5x + 55 = 180$

Step3: Isolate term with x

$5x = 180 - 55$
$5x = 125$

Step4: Solve for x

$x = \frac{125}{5}$

Step5: Calculate $m\angle B$

$m\angle B = 3(25) - 10$

Step6: Calculate $m\angle C$

$m\angle C = 2(25)$

Answer:

$x = 25$
$m\angle B = 65^\circ$
$m\angle C = 50^\circ$