Question

in the figure, (mangle1=(2x)^{circ}) and (mangle2=(x + 96)^{circ}). (a) write an equation to find (x). make sure you use an \=\ sign in your equation: (b) find the degree measure of each angle. (mangle1=square^{circ}) (mangle2=square^{circ})

Explanation:

Step1: Set up the equation

Since $\angle1$ and $\angle2$ are supplementary (they form a straight - line), the sum of their measures is $180^{\circ}$. So the equation is $2x+(x + 96)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+x+96=180$, which gives $3x + 96=180$.

Step3: Solve for $x$

Subtract 96 from both sides: $3x=180 - 96$, so $3x=84$. Then divide both sides by 3: $x=\frac{84}{3}=28$.

Step4: Find the measure of $\angle1$

Substitute $x = 28$ into the expression for $m\angle1$: $m\angle1=2x=2\times28 = 56^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 28$ into the expression for $m\angle2$: $m\angle2=x + 96=28+96 = 124^{\circ}$.

Answer:

(a) Equation: $2x+(x + 96)=180$
(b) $m\angle1 = 56^{\circ}$
$m\angle2 = 124^{\circ}$