Question

1. use the given information to find the measures of the indicated angles.

• (mangle1 = 2x - 30)
• (mangle2 = 5x - 120)
• (mangle3 = 10x - 150)
• (angle1) and (angle3) form a linear pair
• (angle1) and (angle2) are vertical angles

a. draw a diagram in the space below.
b. solve for x and the measure of each angle. write out equation and show work. work must be shown for credit.

x =
(mangle1=)
(mangle2=)
(mangle3=)

Explanation:

Step1: Use vertical - angle property

Since $\angle1$ and $\angle2$ are vertical angles, $m\angle1 = m\angle2$. So, $2x−30 = 5x−120$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $-30=5x - 2x-120$, which simplifies to $-30 = 3x-120$. Then add 120 to both sides: $-30 + 120=3x$, so $90 = 3x$. Divide both sides by 3, we get $x = 30$.

Step3: Find the measure of $\angle1$

Substitute $x = 30$ into the expression for $m\angle1$: $m\angle1=2x - 30=2\times30 - 30=60 - 30=30$.

Step4: Find the measure of $\angle2$

Since $m\angle1 = m\angle2$, $m\angle2 = 30$.

Step5: Find the measure of $\angle3$

Since $\angle1$ and $\angle3$ form a linear - pair, $m\angle1+m\angle3 = 180$. Substitute $m\angle1 = 30$ into the equation: $30+m\angle3 = 180$. Subtract 30 from both sides, we get $m\angle3=180 - 30 = 150$.

Answer:

$x = 30$
$m\angle1 = 30$
$m\angle2 = 30$
$m\angle3 = 150$