Question

angle 6 and angle 7 form a linear pair . Twice the measure of angle 6 is twelve more than four times the measure of angle 7 . Find the measure of each angle

Answer 1

m∠7 = 58°

m∠6 = 122°

Explanation:

Linear Pairs add up to equal 180°.

Step 1: Define

m∠6 + m∠7 = 180°

2m∠6 = 4m∠7 + 12

Step 2: Rewrite systems of equations

I will set m∠6 = x and m∠7 to y

x + y = 180°

2x = 4y + 12

Step 3: Rewrite 2nd equation

2x = 2(2y + 6)

x = 2y + 6

Step 4: Use Substitution

2y + 6 + y = 180

3y + 6 = 180

3y = 174

y = 58°

Step 5: Find x by plugging y back into an original equation

x + 58 = 180

x = 122°

Step 6: Rewrite

x = m∠6

y = m∠7

m∠6 = 122°

m∠7 = 58°