Answer: w = 110° x = 83° y = 87° z = 97°
Step-by-step explanation:
∠(x - 13) and ∠w form a linear pair so their sum is equal to 180°
x - 13 + w = 180 → w = -x + 193
∠(x + 10) and ∠y form a linear pair so their sum is equal to 180°
x + 10 + y = 180 → y = -x + 170
∠x and ∠z form a linear pair so their sum is equal to 180°
x + z = 180 → z = 180 - x
∠x and ∠y and ∠w are the angles of a triangle so their sum equals 180°
x + y + w = 180
x + (-x + 170) + (-x + 193) = 180 Substitution
-x + 263 = 180 Add Like Terms
-x = -83 Subtracted 263 from both sides
x = 83 Divided both sides by -1
w = -x + 193 y = -x + 170 z = 180 - x
w = -83 + 193 y = -83 + 170 z = 180 - 83
w = 110 y = 87 z = 97
