Question

name: lamar greg date: measure. m∠1 = __ m∠18 = m∠2 = m∠19 = m∠3 = m∠20 = m∠4 = m∠21 = m∠5 = m∠22 = m∠6 = m∠23 = m∠7 = m∠24 = m∠8 = m∠25 = m∠9 = m∠26 = m∠10 = m∠27 = m∠11 = m∠28 = m∠12 = m∠29 = m∠13 = m∠30 = m∠14 = m∠31 = m∠15 = m∠32 = m∠16 = m∠33 = m∠17 = __ m∠34 =

Explanation:

Step1: Identify right angle

$m\angle8 = 90^\circ$

Step2: Find $\angle7$ (complementary to $66^\circ$)

$m\angle7 = 90^\circ - 66^\circ = 24^\circ$

Step3: Find $\angle6$ (vertical to $\angle7$)

$m\angle6 = m\angle7 = 24^\circ$

Step4: Find $\angle5$ (supplementary to $66^\circ$)

$m\angle5 = 180^\circ - 66^\circ = 114^\circ$

Step5: Find $\angle3$ (vertical to $66^\circ$)

$m\angle3 = 66^\circ$

Step6: Find $\angle4$ (supplementary to $116^\circ$)

$m\angle4 = 180^\circ - 116^\circ = 64^\circ$

Step7: Find $\angle9$ (vertical to $\angle4$)

$m\angle9 = m\angle4 = 64^\circ$

Step8: Find $\angle10$ (right angle)

$m\angle10 = 90^\circ$

Step9: Find $\angle11$ (complementary to $\angle9$)

$m\angle11 = 90^\circ - 64^\circ = 26^\circ$

Step10: Find $\angle12$ (vertical to $\angle11$)

$m\angle12 = m\angle11 = 26^\circ$

Step11: Find $\angle13$ (vertical to $116^\circ$)

$m\angle13 = 116^\circ$

Step12: Find $\angle1$ (triangle angle sum)

$m\angle1 = 180^\circ - 66^\circ - 64^\circ = 50^\circ$

Step13: Find $\angle2$ (subtract $\angle1$ from $\angle7+\angle11$)

$m\angle2 = (24^\circ+26^\circ) - 50^\circ = 0^\circ$ *Correction: $\angle2 = 180^\circ - 90^\circ - 64^\circ -24^\circ= 2^\circ$ → No, correct: $\angle1+\angle2 = \angle7+\angle11=50^\circ$, so $\angle2=50^\circ - \angle1=0^\circ$ is wrong. Correct: $\angle1 = 180 - (90+66)=24^\circ$, $\angle2=180-(90+64)=26^\circ$ (split of 50°)

Step12 (Revised): Find $\angle1$ (right triangle angle)

$m\angle1 = 90^\circ - 66^\circ = 24^\circ$

Step13 (Revised): Find $\angle2$ (right triangle angle)

$m\angle2 = 90^\circ - 64^\circ = 26^\circ$

Step14: Find $\angle14$ (corresponding to $\angle10$)

$m\angle14 = m\angle10 = 90^\circ$

Step15: Find $\angle15$ (corresponding to $\angle9$)

$m\angle15 = m\angle9 = 64^\circ$

Step16: Find $\angle16$ (corresponding to $\angle11$)

$m\angle16 = m\angle11 = 26^\circ$

Step17: Find $\angle17$ (corresponding to $\angle4$)

$m\angle17 = m\angle4 = 64^\circ$

Step18: Find $\angle18$ (corresponding to $\angle12$)

$m\angle18 = m\angle12 = 26^\circ$

Step19: Find $\angle19$ (corresponding to $\angle11$)

$m\angle19 = m\angle11 = 26^\circ$

Step20: Find $\angle20$ (corresponding to $\angle9$)

$m\angle20 = m\angle9 = 64^\circ$

Step21: Find $\angle21$ (corresponding to $\angle10$)

$m\angle21 = m\angle10 = 90^\circ$

Step22: Find $\angle22$ (supplementary to $\angle21$)

$m\angle22 = 180^\circ - 90^\circ = 90^\circ$

Step23: Find $\angle23$ (corresponding to $\angle13$)

$m\angle23 = m\angle13 = 116^\circ$

Step24: Find $\angle24$ (corresponding to $\angle5$)

$m\angle24 = m\angle5 = 114^\circ$

Step25: Find $\angle25$ (corresponding to $\angle3$)

$m\angle25 = m\angle3 = 66^\circ$

Step26: Find $\angle26$ (corresponding to $\angle6$)

$m\angle26 = m\angle6 = 24^\circ$

Step27: Find $\angle27$ (corresponding to $\angle7$)

$m\angle27 = m\angle7 = 24^\circ$

Step28: Find $\angle28$ (triangle angle sum with $46^\circ$)

$m\angle28 = 180^\circ - 46^\circ - 114^\circ = 20^\circ$

Step29: Find $\angle29$ (vertical to $\angle28$)

$m\angle29 = m\angle28 = 20^\circ$

Step30: Find $\angle30$ (supplementary to $\angle24$)

$m\angle30 = 180^\circ - 114^\circ = 66^\circ$

Step31: Find $\angle31$ (supplementary to $46^\circ$)

$m\angle31 = 180^\circ - 46^\circ = 134^\circ$

Step32: Find $\angle32$ (vertical to $46^\circ$)

$m\angle32 = 46^\circ$

Step33: Find $\angle33$ (supplementary to $\angle31$)

$m\angle33 = 180^\circ - 134^\circ = 46^\circ$

Step34: Find $\angle34$ (vertical to $\angle31$)

$m\angle34 = m\angle31 = 134^\cir…

Answer:

$m\angle1=24^\circ$, $m\angle2=26^\circ$, $m\angle3=66^\circ$, $m\angle4=64^\circ$, $m\angle5=114^\circ$, $m\angle6=24^\circ$, $m\angle7=24^\circ$, $m\angle8=90^\circ$, $m\angle9=64^\circ$, $m\angle10=90^\circ$, $m\angle11=26^\circ$, $m\angle12=26^\circ$, $m\angle13=116^\circ$, $m\angle14=90^\circ$, $m\angle15=64^\circ$, $m\angle16=26^\circ$, $m\angle17=64^\circ$, $m\angle18=26^\circ$, $m\angle19=26^\circ$, $m\angle20=64^\circ$, $m\angle21=90^\circ$, $m\angle22=90^\circ$, $m\angle23=116^\circ$, $m\angle24=114^\circ$, $m\angle25=66^\circ$, $m\angle26=24^\circ$, $m\angle27=24^\circ$, $m\angle28=20^\circ$, $m\angle29=20^\circ$, $m\angle30=66^\circ$, $m\angle31=134^\circ$, $m\angle32=46^\circ$, $m\angle33=46^\circ$, $m\angle34=134^\circ$