For exercises 1-3, use your conjectures to find each angle measure

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°

n

step-by-step explanation:

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05