Question

Use each diagram to solve for x.

(pictures provided)


1. x =

2. x =

Answer 1

see explanation

Explanation:

Since the lines are parallel then

6x + 3 and 45 are alternate angles and congruent, hence

6x + 3 = 45 ( subtract 3 from both sides )

6x = 42 ( divide both sides by 6 )

x = 7

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Since the lines are parallel then

7x - 1 and 5x + 19 are corresponding angles and congruent, hence

7x - 1 = 5x + 19 ( subtract 5x from both sides )

2x - 1 = 19 ( add 1 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

Answer 2

1. Since interior adjacent angles are equal

The angle 6x+3 is equal to 45 degrees

so 6x+3=45 ➡️ 6x=45-3 ➡️ 6x=42

x=42/6, x=7

Ans: x=7 degrees

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2. Since congruent angles are equal

The angle 5x+19= 7x-1

so 5x+19=7x-1 ➡️ 5x+19+1=7x ➡️ 20=7x-5x ➡️ 2x=20

x=20/2=10.

Ans: x=10 degrees