Question

in the figure, m∠1=(2x)° and m∠2=(x + 93)°. (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: Set up the equation

Since $\angle1$ and $\angle2$ are supplementary (form a straight - line), their sum is $180^{\circ}$. So the equation is $2x+(x + 93)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+x+93=3x + 93$. So the equation becomes $3x+93 = 180$.

Step3: Solve for $x$

Subtract 93 from both sides: $3x=180 - 93$, so $3x=87$. Then divide both sides by 3: $x=\frac{87}{3}=29$.

Step4: Find the measure of $\angle1$

Substitute $x = 29$ into the expression for $\angle1$: $m\angle1=2x=2\times29 = 58^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 29$ into the expression for $\angle2$: $m\angle2=x + 93=29+93 = 122^{\circ}$.

Answer:

(a) Equation: $2x+(x + 93)=180$
(b) $m\angle1 = 58^{\circ}$
$m\angle2 = 122^{\circ}$