Question

The measure of angle 4 is 120°, and the measure of angle 2 is 35°.

What is the measure of angle 5?
95°
105°
130°
155°

Answer 1

i believe it's 95 degrees

Answer 2

Answer: The correct option is (A) 95°.

Step-by-step explanation: In the given figure, we have

m∠4 = 120° and m∠2 = 35°.

We are to find the measure of ∠5.

Since ∠3 and ∠4 makes a linear pair, so

`m\angle 3+m\angle 4=180^\circ\\\\\Rightarrow m\angle 3+120^\circ=180^\circ\\\\\Rightarrow m\angle 3=180^\circ-120^\circ\\\\\Rightarrow m\angle 3=60^\circ.`

The sum of the measures of three angles of a triangle is 180°, so

`m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow m\angle 1+35^\circ+60^\circ=180^\circ\\\\\Rightarrow m\angle 1+95^\circ=180^\circ\\\\\Rightarrow m\angle 1=180^\circ-95^\circ\\\\\Rightarrow m\angle 1=85^\circ.`

Again, since ∠1 and ∠5 makes a linear pair, so

`m\angle 1+m\angle 5=180^\circ\\\\\Rightarrow 85^\circ+m\angle 5=180^\circ\\\\\Rightarrow m\angle 5=180^\circ-85^\circ\\\\\Rightarrow m\angle 5=95^\circ.`

Thus, the measure of ∠5 is 95°. Option (A) is correct.