Answer:
10. x = 5; y = 9
Step-by-step explanation:
10.
The sum of the measures of the angles of a triangle is 180.
6y - 5 + 10y - 41 + 12x + 22 = 180
12x + 16y - 24 = 180
12x + 16y = 204
3x + 4y = 51 Equation 1
Two sides are congruent, so opposite angles are congruent.
6y - 5 = 10y - 41
36 = 4y
4y = 36 Equation 2
Equations 1 and 2 form a system, of equations.
3x + 4y = 51
4y = 36
Solve the second equation for y.
y = 9
Substitute 9 for y in the first equation.
3x + 4(9) = 51
3x + 36 = 51
3x = 15
x = 5
Answer: x = 5; y = 9
