In a triangle ,Angle B is twice as large as Angle A. Angle C is five more than Angle B. What are the angle measurements of Angles A, B , and C?

∠ A = 35°, ∠ B = 70°, ∠ C = 75°

Step-by-step explanation:

let ∠ A be x then ∠ B is 2x ( twice as large as A ) and

∠ C is 2x + 5 ( 5 more than B )

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 2x + 2x + 5 = 180, that is

5x + 5 = 180 ( subtract 5 from both sides )

5x = 175 ( divide both sides by 5 )

x = 35

Thus

∠ A = x = 35°

∠ B = 2x = 2 × 35° = 70°

∠ C = 2x + 5 = 70 + 5 = 75°

The angle measurements of the Angles A, B, and C are 35°, 70° and 75° respectively.

Step-by-step explanation:

Sum of all angles in a triangle is = 180°

Therefore, A + B + C = 180° (1)

From the question, the statement shows that;

B = 2A   ==>   A = B/2 (2)

C = 5 + B (3)

Substitute for A and C in equation (1)

(B/2) + B + (5+B) = 180°

B/2 + B + 5 + B = 180°

B/2 + 2B + 5 = 180°

Multiply through by 2

B + 4B + 10 = 360°

5B + 10 = 360°

5B = 360 - 10

5B = 350

B = 70°

Since B is 70°, substitute for B in both equation (2) and (3) to get A and C respectively.

A = B/2   ==> 70/2 = 35°

C = 5 + B ==> 5 + 70 = 75°

To proof A + B + C = 180°

       35° + 70° + 75° =180°

                   180° = 180°

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