Question

Find the value of x in each case Please ASAP

Answer 1

`\boxed{\mathrm{view \: explanation}}`

Explanation:

First problem:

Vertically opposite angles are equal. The angle opposite of 3x is equal to 3x. Angle ACH becomes 2x because 2x + x = 3x.

Angles in triangle add up to 180 degrees.

2x + 2x + 100 = 180

4x = 80

`\boxed{x = 20}`

Second problem:

Alternating angles are equal. Angle RST is x.

Angles in a triangle add up to 180 degrees.

2x + x + x = 180

4x = 180

`\boxed{x=45}`

Answer 2

1. x = 20

2. x = 45

Explanation:

First Picture:

Because of vertical angles theorem, ECD is congruent to ACB making ACH 2x

Since a triangle adds up to 180 we can use the equation 2x + 2x + 100 = 180

From this, you will get x = 20

Second Picture:

Because we know that the lines are parallel you can use alternate interior angles theorem and make RST x too

Like the other problem, we can use an equation

In this case it is x + 2x + x = 180

You should get x = 45