Question

What is the value of x if angles m and n are congruent

Answer 1

Answer:

x = 31

Step-by-step explanation:

TRU = 114 + m + n

TRU = 114 + 33 + 33

m = 33

n = 33

Where T is 114 is part of a linear pair so the other angle would be 66.

S = 31

To find the vertical angle do.

S + T = 31 + 66

ST = 97

To find the vertical angle do

180 - 97 = 83

So the smallest triangle would be

66 + 83 + x = 180 (collect like terms)

149 + x = 180 (minust 149 on both sides)

x = 31

Hope this helps!!

Answer 2

Answer:

x = 64

Step-by-step explanation:

If angles m and n are congruent, we use the triangle RTU to solve for n

m+n+ 114 =180

Since m=n

n+n+114 =180

2n +114=180

2n =66

n =66/2

n = 33

m= 33

Using triangle SUV

31+m+ < SVU = 180

31+33 + < SVU = 180

64 +< SVU = 180

64 -64+< SVU = 180-64

< SVU = 116

We know x + < SVU = 180 since they form a straight line

x + 116 = 180

x = 180-116

x = 64