Answer:
m∠1 = 112°
Consider x and 68° only. They are considered supplementary angles (angles that add up to 180°)
So,
m∠1 + 68 = 180
m∠1 = 180 - 68
m∠1 = 112°
m∠3 = 68°
Do the same thing as m∠1. Consider the two angles that would add up to 180, m∠1 and m∠3.
Since we know m∠1, we can easily solve m∠3.
So,
m∠3 + m∠1 = 180
m∠3 + 112 = 180
m∠3 = 180 - 112
m∠3 = 68
By now, you have noticed, why is the same as the other angle next to m∠1? This is because they are vertical angles. This is called vertical angle congruence theory.
m∠4 = 22
This is almost the same as solving for m∠3 and m∠1. The only difference is we conclude two angles that are complement to each other (angles that add up to 90°)
So,
m∠3 + m∠4 = 90
68° + m∠4 = 90
m∠4 = 90 - 68
m∠4 = 22
m∠5 = 90° (correct)
C.
Find the value of "x"
Just like we solved for the questions above, we arrange them to add up to 180°.
So,
(2x + 11) + (6x - 7) = 180
2x + 11 + 6x - 7 = 180
2x + 6x + 11 - 7 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 ÷ 8
x = 22°
Check:
2x + 11 + 6x - 7 = 180
2(22) + 11 + 6(22) - 7 = 180
44 + 11 + 132 - 7 = 180
55 + 125 = 180
180 = 180 (correct)
Good luck sleeping
