Question

Triangle ABC has angle measrures as shown

(a) what is the value of x? show your work.
(b) what is the measures of the angle C? Show your work

Answer 1

`\text{(a) } x=11,\\\text{(b) } \angle C=12^(\circ)`

Explanation:

The sum of the interior angles in a triangle is always equal to 180 degrees. Therefore, we have the following equation:

`(3x+28)+(5x+52)+(2x-10)=180`

Solving for
`x`:

`(3x+28)+(5x+52)+(2x-10)=180,\\3x+28+5x+52+2x-10=180,\\10x+70=180,\\10x=110,\\x=\boxed{11}`

Substitute
`x=11` to solve for angle C:

`m\angle C=2x-10,\\m\angle C=2(11)-10,\\m\angle C==22-10=\boxed{12^(\circ)}`