Answer:
The internal angles are 78°, 72°, 30°, and the external angle is 150°
Step-by-step explanation:
In a triangle, the measure of an external angle at one vertex equals the sum of the measures of the opposite internal angles to this vertex
In the given figure
∵ The angle of measure (4x + 22) is an exterior angle
∵ The angles of measures (3x - 18) and (2x + 8) are the opposite
interior angles
→ By using the rule above
∴ (3x - 18) + (2x + 8) = (4x + 22)
→ Add the like terms in the left side
∵ (3x + 2x) + (-18 + 8) = 4x + 22
∴ 5x + (-10) = 4x + 22
→ Remember (+)(-) = (-)
∴ 5x - 10 = 4x + 22
→ Add 10 to both sides
∵ 5x - 10 + 10 = 4x + 22 + 10
∴ 5x = 4x + 32
→ Subtract 4x from both sides
∵ 5x - 4x = 4x - 4x + 32
∴ x = 32
→ Substitute the value of x in the external and internal angles to find them
∵ The external angle = 4(32) + 22 = 128 + 22
∴ The external angle = 150°
∵ One of the internal angle = 3(32) - 18 = 96 - 18
∴ One of the internal angle = 78°
∵ Other internal angle = 2(32) + 8 = 64 + 8
∴ Other internal angle = 72°
→ The sum of the measure of the internal angles of a Δ is 180°
∵ The third internal angle of the triangle = 180° - 78° - 72°
∴ The third internal angle of the triangle = 30°
∴ The internal angles are 78°, 72°, 30°, and the external angle is 150°
