Question

Find m∠3 if m∠5=130 and m∠4 =70

Answer 1

m∠5=130 and m∠4 =70
so
m<2 = 180 - m<5
m<2 = 180 - 130
m<2 = 50

m<3 = 180 - (m<2 + m<4)
m<3 = 180 - (50+70)
m<3 = 180 - 120
m<3 = 60

Answer 2

Answer: The required measure of angle 3 is 60°.

Step-by-step explanation: We are given to find the measure of angle 3 from the figure if

m∠5 = 130° and m∠4 = 70°.

Let the measure of angle 3 be x°.

From the figure, we note that

angle 5 is an exterior angle and angles 3 and 4 are two remote interior angles of the triangle.

We know that

the measure of an exterior angle to a triangle is equal to the sum of the measures of two remote interior angles.

So, we get

`m\angle 5=m\angle 3+m\angle 4\\\\\Rightarrow 130^\circ=x+70^\circ\\\\\Rightarrow x=130^\circ-70^\circ\\\\\Rightarrow x=60^\circ.`

Thus, the required measure of angle 3 is 60°.