Answer:
To find c you know that angles on a straight line equal 180° (supplementary angles). So 70+30+∠C=180.
Now we can solve this.
100+c=180.
Move the 100 over to the other side.
100-100+c=180-100
Simplify.
∠C=80°
Because we know that the two lines with double arrows are parallel, we can use the rule that alternate interior angles are congruent. This means that ∠E=70.
∠E=70°
Since the total sum of the angles in a triangle are equal to 180°, we know that ∠D+∠C+∠E=180. Because we already know ∠C and ∠E we can put those numbers in for them. 80°+70°+∠D=180°. Now we can solve this.
80+70+D=180
Simplify this.
150+D=180
Now we move the 150 over to the other side to get D by itself.
150-150+D=180-150
Simplify.
D=30
∠D=30°
Now we can find the vertical angle opposite ∠A by using the alternate interior angles rule again this time using the parallel lines with only one arrow on them. The vertical angle opposite ∠A=30°. Since vertical angles are congruent ∠A=30°.
∠A=30°
We are going to use the alternate angles rule one more time to solve for ∠B (this rule is very important when dealing with parallel lines), we could also use the corresponding angles rule but for simplicity we will just stick with the alternate angles rule. Because the vertical angle opposite ∠A is equal to 30°, we can see that the supplementary angle opposite ∠B=30°. Because this angle is supplementary with B we know that 30+B=180.Now we can solve this.
30+B=180
Now we move the 30 over to the other side.
30-30+B=180-30
Simplify.
B=150
∠B=150°
I hope this helps!