Answer:
y = 58°
z = 122°
Step-by-step explanation:
Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.
Therefore,
(7x + 10) + y = 180
(3x + 10) + z = 180
Alternate interior angle theorem: when 2 parallel lines (AB and CD) are cut by a transversal (EF), the resulting alternate interior angles are equal.
Therefore,
y = (3x + 10)
z = (7x + 10)
Substituting y = (3x + 10) into (7x + 10) + y = 180 and solving for x:
⇒ (7x + 10) + (3x + 10) = 180
⇒ 10x + 20 = 180
⇒ 10x = 160
⇒ x = 16
Calculate angle y and angle z by substituting the found value for x into their equations:
y = 3(16) + 10 = 58°
z = 7(16) + 10 = 122°
