To find the measures of the angles in the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of the three angles in a triangle is always 180°.
Let's assign variables to the angles in the triangle, where angle A is represented by x, angle B is represented by 5x + 4, and angle C is represented by 6x - 3.
According to the Triangle Angle Sum Theorem, the equation is:
A + B + C = 180°
Substituting the variables, we get:
x + (5x + 4) + (6x - 3) = 180°
Now, let's solve this equation for x:
12x + 1 = 180°
12x = 179°
x = 179°/12
To find the measures of the angles, we substitute the value of x back into the expressions for the angles:
A = 4x + 14
A = 4(179°/12) + 14
A ≈ 59°
B = 5x + 4
B = 5(179°/12) + 4
B ≈ 58°
C = 6x - 3
C = 6(179°/12) - 3
C ≈ 63°
Therefore, the measure of the angles in the triangle is approximately 59°, 58°, and 63°.
The correct answer is D. 59°, 58°, and 63°.
B 5x+4 A 4x+14 C 6×-3
Use the Triangle Angle Sum Theorum to find the measure of the angles for the triangle in the diagram?
A. 59°, 63°, and 48°
B. 54°, 44°, and 82°
C. 57°, 54°, and 69°
D. 59°, 58°, and 63°
1 answer