Question

2.) given (mangle1=(10x + 238)^{circ}) and (mangle8=(3x + 154)^{circ}), find (mangle7).

Explanation:

Step1: Identify angle - relationship

$\angle1$ and $\angle8$ are corresponding angles, so $m\angle1 = m\angle8$.
$10x + 238=3x + 154$

Step2: Solve for $x$

Subtract $3x$ from both sides:
$10x-3x + 238=3x-3x + 154$
$7x+238 = 154$
Subtract 238 from both sides:
$7x+238 - 238=154 - 238$
$7x=-84$
Divide both sides by 7:
$x=\frac{-84}{7}=-12$

Step3: Find $m\angle8$

Substitute $x = - 12$ into the expression for $m\angle8$:
$m\angle8=3x + 154=3\times(-12)+154=-36 + 154 = 118^{\circ}$

Step4: Find $m\angle7$

$\angle7$ and $\angle8$ are supplementary (linear - pair), so $m\angle7+m\angle8 = 180^{\circ}$.
$m\angle7=180 - m\angle8$
$m\angle7=180 - 118=62^{\circ}$

Answer:

$62^{\circ}$