Answer:
m<WYZ = 23°
m<ACB = 87°
Step-by-step explanation:
Problem 1: Find WYZ
Given,
m<WVX = (3x - 7)°
m<VYZ = (16x - 3)°
∆WYZ ~ ∆WVX, therefore:
m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)
m<WYZ = (3x - 7)° (substitution)
Create an equation to find the value of x.
m<WYZ + m<VYZ = 180° (linear pair)
(3x -7)° + (16x - 3)° = 180° (substitution)
Solve for x
3x - 7 + 16x - 3 = 180
Add like terms
19x - 10 = 180
Add 10 to both sides
19x - 10 + 10 = 180 + 10
19x = 190
Divide both sides by 19
19x/19 = 190/19
x = 10
m<WYZ = (3x - 7)
Substitute x = 10
m<WYZ = 3(10) - 7 = 30 - 7
m<WYZ = 23°
Problem 2: Find m<ACB
Given,
m<A = 62°
m<AED = (11x - 2)°
m<B = (6x + 13)°
∆ADE ~ ∆ACB, therefore:
m<AED = m<B (corresponding angles of similar ∆s are congruent)
(11x - 2)° = (6x + 13)°
Solve for x
11x - 2 = 6x + 13
Collect like terms
11x - 6x = 2 + 13
5x = 15
Divide both sides by 5
5x/5 = 15/5
x = 3
m<ACB + m<B + m<A = 180° (sum of ∆)
m<ACB + (6x + 13) + 62° = 180° (substitution)
Plug in the value of x and solve
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (18 + 13) + 62° = 180°
m<ACB + 31° + 62° = 180°
m<ACB + 93° = 180°
Subtract 93 from both sides
m<ACB = 180° - 93°
m<ACB = 87°
