In △ABC, m∠A = (4x + 5)° and m∠B = (5x−1)°. What is m∠C? Question 3 options: 6° 180° 122° 29°

Question

Can someone please solve this?

Answer 1

Good morning, Christiaan,

First step is to remember that all three interior angles on any triangle must equal 180 degrees, okay? 

Second, you are given the measures of two angles with the third missing. 

Let's solve, okay? 

(4x + 5) + (5x -1) + x = 180   ......x is for the third angle which was not given.

Now simplify. 

4x + 5 + 5x -1 + x = 180 

Combine like terms. 

10x + 4 = 180 ....solve for x 

 

10x = 176
x = 17.6 


Now, plug the value of x into each of the given angle measures, okay? 

4 * 17.6 + 5 = 75.4 degrees 
5 * 17.6 - 1 = 87 degrees 

Proof your work. 

When adding the two given angles and subtracting the total you should have the original value of x = 17.6 degrees since again all three interior angles must equal 180 degrees. 

75.4 + 87 + x = 180 ...solve for x 

162.4 + x = 180....subtract 162.4 from both sides of equation

x = 17.6  

It proofs. I hope this assists you and that you have a great day today. If you have any further questions, or comments, please place in the comment section below. 

PLEASE NOTE: If you plug the value of 17.6 into the above for each time an x appears in an angle it will also proof. 

Given the data you provided, this is the only possible answer and it does not fit one of the four answers you provided us. If I am still missing a piece of information, please provide so we can ensure you have the correct solution. Many thanks in advance.