Question

On line l, m∠p = 21x +25 and m∠n = \{675x\:-27}/3 Use this information to answer Part A & B below. Part A: Determine the value of x. Part B: Determine the measure of ∠p and ∠n in degrees. p = n =

Answer 1

a) x = 492/738

b) m<p = 39°

m<n = 141°

Explanation:

Find the diagram attached

a) The sum of angle on the straight line l is 180degrees

m<n + m<p = 180 degrees

Given

<p = 21x+25

<n = (675x-27)/3

Substitute the given values into the formula

(675x-27)/3 + 21x+25= 180

[(675x-27+3(21x+25))]/3 = 180

675x-27+63x +75 = 180*3

675x+63x-27+75 = 540

738x+48 = 540

738x = 540 - 48

738x = 492

x = 492/738

b) m<p = 21x+25

m<p = 21(492/738) + 25

m<p = 14+25

m<p = 39°

Recall that m<p + m<n = 180

m<n = 180-m<p

m<n = 180 -39

m<n = 141°