Question

in the figure, m∠1=(2x)° and m∠2=(x + 87)°. (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. m∠1=° m∠2=°

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), their sum is $180^{\circ}$. So the equation is $2x+(x + 87)=180$.

Step2: Simplify the equation

Combine like - terms: $2x+x+87 = 180$, which simplifies to $3x+87 = 180$.

Step3: Solve for x

Subtract 87 from both sides: $3x=180 - 87$, so $3x = 93$. Then divide both sides by 3: $x=\frac{93}{3}=31$.

Step4: Find the measure of $\angle1$

Substitute $x = 31$ into the expression for $\angle1$: $m\angle1=2x$. So $m\angle1=2\times31 = 62^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 31$ into the expression for $\angle2$: $m\angle2=x + 87$. So $m\angle2=31+87 = 118^{\circ}$.

Answer:

(a) Equation: $2x+(x + 87)=180$
(b) $m\angle1 = 62^{\circ}$
$m\angle2 = 118^{\circ}$