Question

Help me please TT,,,,,

Answer 1

Answer:

The value of ∠A is 62° ⇒ c

The value of ∠B is 54°⇒ d

Step-by-step explanation:

In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.

In Δ ABC

∵ The measure of the exterior angle at the vertex C = 116°

∵ The opposite interior angles to vertex C are ∠A and ∠B

∵ m∠A = (3x - 13)°

∵ m∠B = (2x + 4)°

→ By using the rule above

∴ (3x - 13) + (2x + 4) = 116

→ Add the like terms in the left side

∵ (3x + 2x) + (-13 + 4) = 116

∴ 5x + -9 = 116

∴ 5x - 9 = 116

→ Add 9 to both sides

∵ 5x - 9 + 9 = 116 + 9

∴ 5x = 125

→ Divide both sides by 5

∴ x = 25

→ To find the measures of angle A and B substitute x in their

   measures by 25

∵ m∠A = 3(25) - 13 = 75 - 13

∴ m∠A = 62°

∴ The value of ∠A is 62°

∵ m∠B = 2(25) + 4 = 50 + 4

∴ m∠B = 54°

∴ The value of ∠B is 54°