Question

Please answer the picture below.

Answer 1

`\displaystyle \boxed{20}° = ∠x`

Step-by-step explanation:

Since we have two parallel lines, therefore the measure of angle B is a right angle [90°]. Then you automatically would see that the measure of angle C is 70°, according to the Vertical Angles Theorem. Then you use the Triangular Interior Angles Theorem to find the
`\displaystyle m∠x:`

180° = 70° + 90° + m∠A

180° = 160° + m∠A

- 160° - 160°

______________

`\displaystyle 20° = m∠A`

The m∠A is 20°, therefore the m∠x is also 20°, according to the Vertical Angles Theorem.

I am joyous to assist you anytime.

Answer 2

m < x = 20 degrees.

Explanation:

m < ACB = m < GCJ = 70 degrees ( opposite angles).

m < ABC = 90 degrees ( because DE is parallel to FG and KL is perpendicular to FG).

So triangle ABC is a right angled triangle.

Therefore m < BAC = 90 - m < ACB

m < BAC = 90 - 70 = 20 degrees.

Finally m < x = m < BAC = 20 degrees (opposite angles).