Chapter 10.5, Problem 54STP

To determine

Find the value of a +b + c =?

Answer to Problem 54STP

Option C is correct.

Explanation of Solution

Given:

  

Concept Used:

In any triangle, the sum of three angles is ${180}^0$ , so we can write: $x+y+z={180}^0$

  

Calculation:

We know that the linear pair is ${180}^0$

In this figure there are 3 pairs of linear pair:

  $\begin{array}{l}a+x={180}^0\\ b+y={180}^0\\ c+z={180}^0\end{array}$

  $a+x+b+y+c+z={180}^0+{180}^0+{180}^0={540}^0$

In any triangle, the sum of three angles is ${180}^0$ , so we can write: $x+y+z={180}^0$

  $a+b+c=(a+x+b+y+c+z)-(x+y+z)={540}^0-{180}^0={360}^0$

  $a+b+c={360}^0$

Thus, $a+b+c={360}^0$ Option C is correct.