Question

Please I'm GIVING 40 POINTS FOR REAL ANSWER

3. Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.

A) 2(x + 15) B) 3x+10 C) 5x

(a) Identify the angle relationship and set up your equation with the given expressions.
(b) What is the value of x? Show your work.
(c) What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.

Answer 1

I hope its right...

Explanation:

Part A)

A + B + C = 180 and now replace with the algebraic expressions given for each angle:

2(x + 15) + 3 x + 10 + 5 x = 180n eliminate parenthesis 2 x + 30 + 3 x + 10 + 5 x = 180

Part B)

2 (x+15) + 3x + 10+ 5x = 180 2x + 30 + 3x + 10 +5x = 180 10 +40 = 180

- 40 -40 10x divided by 10 = 140 divided by 10 x= 14

Part C)

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

Answer 2

x = 14

< A = 58 degrees

< B = 52 degrees

< C = 70 degrees

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