Question

for exercises 4 - 6, use the figure at the right. question 4 1 pts if $ellparallel m$, what is $mangle1$? 22 122 58 130

Explanation:

Step1: Identify angle - relationship

Since $\ell\parallel m$, the angles $(2x + 14)^{\circ}$ and $(5x+12)^{\circ}$ are alternate - interior angles, so they are equal.
$2x + 14=5x + 12$

Step2: Solve the equation for x

Subtract $2x$ from both sides: $14 = 3x+12$.
Subtract 12 from both sides: $3x=14 - 12=2$.
Divide both sides by 3: $x=\frac{2}{3}$.

Step3: Find the measure of an angle

We know that $\angle1$ and $(2x + 14)^{\circ}$ are supplementary (linear - pair).
First, find the measure of $(2x + 14)^{\circ}$ by substituting $x = \frac{2}{3}$ into it:
$2x+14=2\times\frac{2}{3}+14=\frac{4}{3}+14=\frac{4 + 42}{3}=\frac{46}{3}
eq$ a valid angle measure.
Let's assume the angles are corresponding angles. Then $2x + 14+5x + 12=180$ (co - interior angles are supplementary when $\ell\parallel m$).
Combine like terms: $7x+26 = 180$.
Subtract 26 from both sides: $7x=180 - 26 = 154$.
Divide both sides by 7: $x = 22$.

Step4: Calculate the measure of $\angle1$

The angle $(2x + 14)^{\circ}$, substituting $x = 22$, we get $2\times22+14=44 + 14=58^{\circ}$.
$\angle1$ and $(2x + 14)^{\circ}$ are supplementary. So $m\angle1=180-(2x + 14)$.
Substituting $x = 22$, $m\angle1=180 - 58=122^{\circ}$.

Answer:

$122$