Part 1)

Find m∠a

m∠a=54° --------> by vertical angles

Find m∠b

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

Find m∠c

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

or

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

therefore

the answer part 1) is equal to

a) the measure of angle a is 54°

b) the measure of angle b is 54°

c) the measure of angle c is 54°

Part 2)

Find m∠d

we know that

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

Find m∠c

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°

Find m∠b

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

Find m∠a

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

the answer Part 2) is

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°

Part 3)

Let

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

Find m∠x

we know that

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

Find m∠a

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

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

Find m∠b

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

m∠b=72°+54°-------> m∠b=126°

therefore

the answer Part 3) is

a) The measure of angle a is 72°

b) The measure of angle b is 126°

c) The measure of angle x is 54°

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