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Flura [38]
3 years ago
6

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?
Mathematics
2 answers:
777dan777 [17]3 years ago
5 0

Answer:

∠ 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°

sesenic [268]3 years ago
5 0

Answer:

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 = <em>B/2 </em><em> </em>.............<em> </em>(2)

C = <em>5 + B</em><em> </em>..................................... (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°

<em>To proof A + B + C = 180°</em>

<em>        35° + 70° + 75° =180°</em>

<em>                    180° = 180°</em>

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