Question

Find the measures. With steps please. ​

Answer 1

Answer:

sum of the given angles = 180°

12+5x+17x+4=180°

16+22x=180°

22x=164°

x=164°/22

x=7.45

substitute

to verify

12+5(7.45)+17(7.45)+4

12+37.25+126.65+4

16+163.9=179.9 ~ 180°

Answer 2

$\underline{\text{Given:}}$

$\text{See Attached diagram in the question}$

$\underline{\text{To Find:}}$

$\text{The measure of the angles}$

$\underline{\text{Explanation: }}$

$\text{Line l and line m are parallel lines}$

$\Longrightarrow \text{The two angles are alternate angles on a pair of parallel lines}$

$\Longrightarrow \text{The two angles are equal}$

$\underline{\text{Solve x:}}$

$12 + 5x = 17x + 4$

$17x - 5x = 12 - 4$

$12x = 8$

$x = \dfrac{2}{3}$

$\underline{\text{Find the angles:}}$

$\text{Angle } = 12 + 5x$

$\text{Angle } = 12 + 5(\dfrac{2}{3} )$

$\text{Angles } = 15\dfrac{1}{3} ^\circ \text{ ( or } 15.3^\circ \text{)}$

$\text {Both angles are equal}$

$\Longrightarrow \text{The two angles are both 15.3}^\circ$

$\boxed{\boxed {\textbf{The two angles are both 15.3}^\circ}}$