Question

example 5
if ( mangle12 = 121^circ ) and ( mangle6 = 75^circ ), find each
a. ( mangle1 = )
e. ( mangle5 = )
i. ( mangle10 = )
b. ( mangle2 = )
f. ( mangle7 = )
j. ( mangle11 = )
c. ( mangle3 = )
g. ( mangle8 = )
k. ( mangle13 = )
d. ( mangle4 = )
h. ( mangle9 = )
l. ( mangle14 = )
find each measure.

Explanation:

Step1: Find $\angle 1$, vertical to $\angle 3$

$\angle 1$ and $\angle 12$ are same-side interior angles, so $m\angle 1 = 180^\circ - m\angle 12 = 180^\circ - 121^\circ = 59^\circ$

Step2: Find $\angle 2$, linear pair with $\angle 1$

$m\angle 2 = 180^\circ - m\angle 1 - m\angle 6 = 180^\circ - 59^\circ - 75^\circ = 46^\circ$

Step3: Find $\angle 3$, vertical to $\angle 1$

$m\angle 3 = m\angle 1 = 59^\circ$

Step4: Find $\angle 4$, vertical to $\angle 6$

$m\angle 4 = m\angle 6 = 75^\circ$

Step5: Find $\angle 5$, vertical to $\angle 2$

$m\angle 5 = m\angle 2 = 46^\circ$

Step6: Find $\angle 7$, corresponding to $\angle 1$

$m\angle 7 = m\angle 1 = 59^\circ$

Step7: Find $\angle 8$, corresponding to $\angle 2$

$m\angle 8 = m\angle 2 = 46^\circ$

Step8: Find $\angle 9$, corresponding to $\angle 3$

$m\angle 9 = m\angle 3 = 59^\circ$

Step9: Find $\angle 10$, corresponding to $\angle 6$

$m\angle 10 = m\angle 6 = 75^\circ$

Step10: Find $\angle 11$, vertical to $\angle 12$

$m\angle 11 = m\angle 12 = 121^\circ$

Step11: Find $\angle 12$, given value

$m\angle 12 = 121^\circ$

Step12: Find $\angle 13$, vertical to $\angle 1$

$m\angle 13 = m\angle 1 = 59^\circ$

Step13: Find $\angle 14$, vertical to $\angle 6$

$m\angle 14 = m\angle 6 = 75^\circ$

Answer:

a. $m\angle 1 = 59^\circ$
b. $m\angle 2 = 46^\circ$
c. $m\angle 3 = 59^\circ$
d. $m\angle 4 = 75^\circ$
e. $m\angle 5 = 46^\circ$
f. $m\angle 7 = 59^\circ$
g. $m\angle 8 = 46^\circ$
h. $m\angle 9 = 59^\circ$
i. $m\angle 10 = 75^\circ$
j. $m\angle 11 = 121^\circ$
k. $m\angle 13 = 59^\circ$
l. $m\angle 14 = 75^\circ$