Question

# The parallel lines at the right are cut by a transversal. Find the value of x. a. Angles 1 and 2 are corresponding angles, m∠1 = 45°, and m∠2 = (x + 25)°. b. Angles 3 and 4 are alternate interior angles, m∠3 = 2x°, and m∠4 = 80°.

Linear equations and graphs
The parallel lines at the right are cut by a transversal. Find the value of x.
a. Angles 1 and 2 are corresponding angles, $$\displaystyle{m}∠{1}={45}°$$, and $$\displaystyle{m}∠{2}={\left({x}+{25}\right)}°$$.
b. Angles 3 and 4 are alternate interior angles, $$\displaystyle{m}∠{3}={2}{x}°$$, and $$\displaystyle{m}∠{4}={80}°$$.

2021-01-03
a.Since then lines are parallel, then corresponding angles are congruent and thus, have the same measure:
$$\displaystyle{m}∠{1}={m}∠{2}$$
45=x+25
20=x
or
x=20
b.Since then lines are parallel, then alternate interior angles are congruent and thus, have the same measure:
$$\displaystyle{m}∠{3}={m}∠{4}$$
2x=80
x=40