Question

Two lines intersect to form a linear pair with equal measures. One angle has the measure 3x° and the other angle has the measure (8y − 70)°. Find the values of x and y.

Answer 1

Substitute by equation 1 in equation 2:

3x+3x = 180

6x = 180

x = 30

Substitute with the value of x in equation 1 to get y as follows:

3x = 8y-70

3(30) + 70 = 8y

160 = 8y

y = 20

Answer 2

The sum of a linear pair of angles is 180 degrees.

Now, we are given two pieces of information. We will use these to develop equations and then solve the equations simultaneously.

First, we know that the two angles are equal, therefore:
3x = 8y-70.............> equation 1
Second, we know that the two angles form a linear pair of angles, therefore:
3x+8y-70 = 180 ......................> equation 2

Substitute by equation 1 in equation 2:
3x+3x = 180
6x = 180
x = 30

Substitute with the value of x in equation 1 to get y as follows:
3x = 8y-70
3(30) + 70 = 8y
160 = 8y
y = 20

Therefore:
the first angle = 3x = 3(30) = 90 degrees
the second angle = 8(20)-70 = 90 degrees
You can notice that the two angles are equal and their sum is 180 as mentioned previously.