Question

In the diagram shown, <1=<4 and<2=<3 The sum of the measures of the four angles is 140 The measure of <3 is 8 less than the measure of <4 What is the combined measure of angles 2, 3, and 4? A. 101° B. 107° C. 109° D. 117°

Answer 1

Answer: Option 'B' is correct.

Explanation:

Since we have given that

∠1 = ∠4

∠2 = ∠3

And sum of the measures of the four angles = 140°

According to question, it becomes,

`\angle 1+\angle 2+\angle 3+\angle 4=140^\circ`

Measure of ∠3 is 8 less than the measure of ∠4.

Let the measure of ∠4 be 'x'.

So, the measure of ∠3 would be 'x-8'.

∠1 = x and ∠2 = x-8

So, put all the values in the above equation:

`x+x+x-8+x-8=140^\circ\\\\4x-16=140^\circ\\\\4x=140+16\\\\4x=156^\circ\\\\x=(156)/(4)\\\\x=39^\circ`

So,

`\angle 2=39-8=31^\circ\\\\\angle 3=39-8=31^\circ\\\\\angle 1=x=39^\circ`

So,
`\angle 2+\angle 3+\angle 4=31^\circ+31^\circ+39^\circ=101^\circ`

Hence, Option 'B' is correct.