Question

50 POINTS! CORRECT AND EXPLANITORY ANSWERS ONLY!

Answer 1

Answer:

A)  Sum of interior angles of a triangle = 180°

⇒ 3(x + 5) + 5x + 15 + 7x = 180

B)  x = 10

C)  m∠A = 45°

     m∠B = 65°

      m∠C = 70°

Step-by-step explanation:

Given:

• m∠A = 3(x + 5)
• m∠B = 5x + 15
• m∠C = 7x

A)  Sum of interior angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180

⇒ 3(x + 5) + 5x + 15 + 7x = 180

B) 3(x + 5) + 5x + 15 + 7x = 180

⇒ 3x + 15 + 5x + 15 + 7x = 180

⇒ 15x + 30 = 180

⇒ 15x = 150

⇒ x = 10

C) m∠A = 3(x + 5) = 3(10 + 5) = 3 x 15 = 45°

    m∠B = 5x + 15 = (5 x 10) + 15 = 50 + 15 = 65°

    m∠C = 7x = 7 x 10 = 70°

Answer 2

Answer:

x = 14

< A = 58 degrees

< B = 52 degrees

< C = 70 degrees

Step-by-step explanation:

Recall that the addition of the three internal angles of a triangle must render 180 degrees, then we can write:

<A + <B + <C = 180

and now replace with the algebraic expressions given for each angle:

2(x + 15) + 3 x + 10 + 5 x = 180

eliminate parenthesis

2 x + 30 + 3 x + 10 + 5 x = 180

combine like terms

10 x + 40 = 180

subtract 40 from both sides

10 x = 140

divide both sides y 10 to isolate x

x = 14

Now that we know x, we can calculate each of the angles using the fiven expressions:

< A = 2 (x + 15) = 2 (14 + 15) = 2 * 29 = 58 degrees

< B = 3 x + 10 = 3 * 14 + 10 = 52 degrees

< C = 5 x = 5 * 14 = 70 degrees