To find the measure of the angles, we add up the measures of all three angles in the triangle and set it equal to 180°.
Given:
Angle BAC = 5x + 4
Angle ABC = 4x + 14
Angle ACB = 6x - 3
Adding up the measures and setting equal to 180°:
(5x + 4) + (4x + 14) + (6x - 3) = 180
Combining like terms:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now, plug x = 11 back into the original expressions for the angles to find their measures:
Angle BAC = 5x + 4 = 5(11) + 4 = 55 + 4 = 59°
Angle ABC = 4x + 14 = 4(11) + 14 = 44 + 14 = 58°
Angle ACB = 6x - 3 = 6(11) - 3 = 66 - 3 = 63°
Therefore, the measure of the angles for the triangle is:
A. 59°, 58°, and 63°
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
(BAC) B. 5x+4 at the top corner, A. 4x+14 at the bottom left, and C. 6x-3 on the right side
A. 59°, 63°, and 48°
B. 54°, 44°, and 82°
C. 59°, 58°, and 63°
D. 57°, 54°, and 69°
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