<u>Part 1) </u>

<u>Find m∠a</u>

m∠a=54° --------> by vertical angles

<u>Find m∠b</u>

m∠b=54° --------> by corresponding angles

<u>Find m∠c</u>

m∠c=m∠a=54°-----> by corresponding angles

or

m∠c=m∠b=54° --------> by vertical angles

therefore

<u>the answer part 1) is equal to</u>

**a) the measure of angle a is 54°**

**b) the measure of angle b is 54°**

**c) the measure of angle c is 54°**

<u>Part 2) </u>

<u>Find m∠d</u>

we know that

m∠d=65° --------> by corresponding angles

<u>Find m∠c</u>

m∠d+m∠c=180° -----> by supplementary angles

solve for m∠c

m∠c=180-m∠d-------> m∠c=180-65°=115°

m∠c=115°

<u>Find m∠b</u>

m∠b=m∠d=65° -------> by alternate exterior angles

<u>Find m∠a</u>

we know that

m∠a+m∠b=180 -------> by consecutive interior angles

m∠a=180- m∠b---------> m∠a=180- 65-----> m∠a=115°

therefore

<u>the answer Part 2) is </u>

a) **The measure of angle a is 115°**

b) **The measure of angle b is 65°**

c) **The measure of angle c is 115°**

d) **The measure of angle d is 65°**

<u>Part 3) </u>

Let

x--------> the angle unknown ( see the attached figure to better understand the problem)

<u>Find m∠x</u>

we know that

m∠x=54° -------> by corresponding angles

<u>Find m∠a</u>

(2*m∠x)+(m∠a)=180 -------> by supplementary angles

m∠a=180-2*m∠x------> m∠a=180-2*54°----->m∠a=72°

<u>Find m∠b</u>

(m∠a+m∠x)=m∠b ------> by corresponding angles

m∠b=72°+54°-------> m∠b=126°

therefore

<u>the answer Part 3) is</u>

a) **The measure of angle a is 72°**

b) **The measure of angle b is 126°**

c) **The measure of angle x is 54°**