Question

in exercises 9 - 30, find the measure of the angle. (the angle number is the exercise number.) assume that lines in each figure that do not intersect are parallel. code key true n false e 43° s 50° t 60° b 65° c 70° d 90° i 114° l 115° g 120° f 137° h geometry concepts: parallel lines

Explanation:

Step1: Solve ∠9 (vertical angle)

∠9 is vertical to 66°, so $m\angle9 = 66^\circ$

Step2: Solve ∠10 (supplementary to 66°)

$\angle10 + 66^\circ = 180^\circ$, so $m\angle10 = 180^\circ - 66^\circ = 114^\circ$

Step3: Solve ∠11 (corresponding to 66°)

∠11 is corresponding to 66°, so $m\angle11 = 66^\circ$

Step4: Solve ∠12 (corresponding to ∠10)

∠12 is corresponding to ∠10, so $m\angle12 = 114^\circ$

Step5: Solve ∠13 (vertical to ∠11)

∠13 is vertical to ∠11, so $m\angle13 = 66^\circ$

Step6: Solve ∠14 (vertical to 137°)

∠14 is vertical to 137°, so $m\angle14 = 137^\circ$

Step7: Solve ∠15 (supplementary to 137°)

$\angle15 + 137^\circ = 180^\circ$, so $m\angle15 = 180^\circ - 137^\circ = 43^\circ$

Step8: Solve ∠16 (vertical to ∠15)

∠16 is vertical to ∠15, so $m\angle16 = 43^\circ$

Step9: Solve ∠17 (right angle)

∠17 is a right angle, so $m\angle17 = 90^\circ$

Step10: Solve ∠18 (vertical to ∠17)

∠18 is vertical to ∠17, so $m\angle18 = 90^\circ$

Step11: Solve ∠19 (supplementary to ∠17)

$\angle19 + 90^\circ = 180^\circ$, so $m\angle19 = 90^\circ$

Step12: Solve ∠20 (supplementary to 115°)

$\angle20 + 115^\circ = 180^\circ$, so $m\angle20 = 180^\circ - 115^\circ = 65^\circ$

Step13: Solve ∠21 (corresponding to ∠20)

∠21 is corresponding to ∠20, so $m\angle21 = 65^\circ$

Step14: Solve ∠22 (corresponding to 115°)

∠22 is corresponding to 115°, so $m\angle22 = 115^\circ$

Step15: Solve ∠23 (vertical to 115°)

∠23 is vertical to 115°, so $m\angle23 = 115^\circ$

Step16: Solve ∠24 (vertical to 47°)

∠24 is vertical to 47°, so $m\angle24 = 47^\circ$

Step17: Solve ∠25 (complementary to 47°)

$\angle25 + 47^\circ = 90^\circ$, so $m\angle25 = 90^\circ - 47^\circ = 43^\circ$

Step18: Solve ∠26 (supplementary to 47°)

$\angle26 + 47^\circ = 180^\circ$, so $m\angle26 = 180^\circ - 47^\circ = 133^\circ$

Step19: Solve ∠27 (vertical to 60°)

∠27 is vertical to 60°, so $m\angle27 = 60^\circ$

Step20: Solve ∠28 (corresponding to 50°)

∠28 is corresponding to 50°, so $m\angle28 = 50^\circ$

Step21: Solve ∠29 (corresponding to ∠27)

∠29 is corresponding to ∠27, so $m\angle29 = 60^\circ$

Step22: Solve ∠30 (corresponding to ∠26)

∠30 is corresponding to the angle supplementary to 50°, so $m\angle30 = 180^\circ - 50^\circ = 130^\circ$

Answer:

$m\angle9=66^\circ$, $m\angle10=114^\circ$, $m\angle11=66^\circ$, $m\angle12=114^\circ$, $m\angle13=66^\circ$
$m\angle14=137^\circ$, $m\angle15=43^\circ$, $m\angle16=43^\circ$
$m\angle17=90^\circ$, $m\angle18=90^\circ$, $m\angle19=90^\circ$
$m\angle20=65^\circ$, $m\angle21=65^\circ$, $m\angle22=115^\circ$, $m\angle23=115^\circ$
$m\angle24=47^\circ$, $m\angle25=43^\circ$, $m\angle26=133^\circ$
$m\angle27=60^\circ$, $m\angle28=50^\circ$, $m\angle29=60^\circ$, $m\angle30=130^\circ$