Answer:
m∠T = 79°
m∠V = 14°
Step-by-step explanation:
Given
As the sum of measures of the angles is 93°.
so
m∠T + m∠V = 93°
(2x + 85)° + (5x + 29)° = 93°
Remove parentheses
[tex]2x+85+5x+29=93[/tex]
[tex]7x+114=93[/tex]
Subtract 114 from both sides
[tex]7x+114-114=93-114[/tex]
Simplify
[tex]7x=-21[/tex]
Divide both sides by 7
[tex]\frac{7x}{7}=\frac{-21}{7}[/tex]
simplify
[tex]x=-3[/tex]
Determining m∠T
m∠T = (2x + 85)°
substitute x = -3
m∠T = (2(-3) + 85)°
= -6 + 85
= 79°
Thus, we conclude that m∠T = 79°
Determining m∠V
m∠V = (5x + 29)°
substitute x = -3
m∠T = (5(-3) + 29)°
= -15 + 29
= 14°
Thus, we conclude that m∠V = 14°
VERIFICATION:
m∠T + m∠V = 93°
substitute m∠T = 79° and m∠V = 14°
79° + 14° = 93°
93° = 93°
L.H.S = R.H.S
