Use the triangle theory to find the measures of the angles for the triangle in the diagram. 5X plus 44X +14 six X subtract three.
To find the measures of the angles in the triangle, we will first set up an equation using the information given.
Let's call the three angles of the triangle A, B, and C.
The information given is:
Angle A: 5X + 44X
Angle B: 14
Angle C: 6X - 3
According to the triangle sum theorem, the sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, we can set up the equation:
Angle A + Angle B + Angle C = 180
(5X + 44X) + 14 + (6X - 3) = 180
Combine like terms:
49X + 14 + 6X - 3 = 180
55X + 11 = 180
Subtract 11 from both sides:
55X = 169
Divide both sides by 55:
X = 169/55
Now that we have the value of X (approximately 3.073), we can substitute it back into the expressions for Angle A, Angle B, and Angle C to find their measures.
Angle A = 5X + 44X = 5(3.073) + 44(3.073)
= 15.365 + 134.932
= 150.297 degrees
Angle B = 14
Angle C = 6X - 3 = 6(3.073) - 3
= 18.438 - 3
= 15.438 degrees
Therefore, the measures of the angles in the triangle are approximately:
Angle A ≈ 150.297 degrees
Angle B ≈ 14 degrees
Angle C ≈ 15.438 degrees