PLEASE HELP ME
Determine the internal and external angles of the triangle below

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°

step-by-step explanation: