Question

in the figure, (mangle1=(2x)^{circ}) and (mangle2=(x + 84)^{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: Use angle - addition property

Since $\angle1$ and $\angle2$ form a straight - line, their sum is $180^{\circ}$. So the equation is $2x+(x + 84)=180$.

Step2: Combine like terms

$2x+x+84 = 180$ simplifies to $3x+84 = 180$.

Step3: Isolate the variable term

Subtract 84 from both sides: $3x=180 - 84$, so $3x = 96$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{96}{3}=32$.

Step5: Find the measure of $\angle1$

Substitute $x = 32$ into the expression for $\angle1$: $m\angle1=2x=2\times32 = 64^{\circ}$.

Step6: Find the measure of $\angle2$

Substitute $x = 32$ into the expression for $\angle2$: $m\angle2=x + 84=32+84 = 116^{\circ}$.

Answer:

(a) Equation: $2x+(x + 84)=180$
(b) $m\angle1 = 64^{\circ}$
$m\angle2 = 116^{\circ}$