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 m∠B and m∠C.



Enter your answers in the boxes.

x =

m∠B=
º

m∠C= ​
º

Answer 1

Answer:

Part 1) $x=25$

Part 2) $m\angle B=65^o$

Part 3) $m\angle C=50^o$

Step-by-step explanation:

step 1

Find the value of x

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle ABC

$m\angle A+m\angle B+m\angle C=180^o$

substitute the given values

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

Solve for x

$(5x+55)^o=180^o$

$5x=180-55\\5x=125\\x=25$

step 2

Find the measure of angle B

we know that

$m\angle B=(3x-10)^o$

substitute the value of x

$m\angle B=(3(25)-10)=65^o$

step 3

Find the measure of angle C

we know that

$m\angle C=(2x)^o$

substitute the value of x

Answer 2

Answer:

Part 1) x=25

Part 2) m\angle B=65^o

Part 3) m\angle C=50^o

Step-by-step explanation: