Question

in the figure, (mangle1=(2x)^{circ}) and (mangle2=(x + 78)^{circ}). (a) write an equation to find (x). make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. (mangle1= ^{circ}) (mangle2= ^{circ})

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary, $2x+(x + 78)=180$.

Step2: Solve for x

Combine like - terms: $3x+78 = 180$. Then $3x=180 - 78=102$, so $x = 34$.

Step3: Find angle measures

$m\angle1=2x=2\times34 = 68^{\circ}$, $m\angle2=x + 78=34+78 = 112^{\circ}$.

Answer:

(a) $2x+(x + 78)=180$
(b) $m\angle1 = 68^{\circ}$
$m\angle2 = 112^{\circ}$