The top of the triangle is 5x + 4 the left side of the triangle is 4x + 14 the right side of the triangle is 6x - 3 Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
(1 point)
A. 59°, 63°, and 48°
B. 57°, 54°, and 69°
C. 59°, 58°, and 63°
D. 54°, 44°, and 82°
To find the measure of the angles in the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180°.
Let's label the angles in the triangle as A, B, and C, corresponding to the top, left side, and right side of the triangle, respectively.
We know that the top of the triangle is 5x + 4, the left side is 4x + 14, and the right side is 6x - 3.
Using the Triangle Angle Sum Theorem, we can set up the equation:
(5x + 4) + (4x + 14) + (6x - 3) = 180
Combine like terms:
15x + 15 = 180
Subtract 15 from both sides:
15x = 165
Divide both sides by 15:
x = 11
Now we can substitute the value of x back into the expressions for the angles:
A = 5x + 4 = 5(11) + 4 = 55 + 4 = 59°
B = 4x + 14 = 4(11) + 14 = 44 + 14 = 58°
C = 6x - 3 = 6(11) - 3 = 66 - 3 = 63°
Therefore, the measure of the angles for the triangle in the diagram is:
A. 59°, 58°, and 63°.