Question

1. Determine the measure of each unknown angle using the diagram below. h 4 a. m 2 = b. m 3 = c. m_4= 3 2 106°

Answer 1

From the properties of Vertically Opposite Angles we can find the value of angle 2, 3 and angle 4:

VERTICALLY OPPOSITE ANGLE : When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

In the given figure, angle 3 and 2 are vertically opposite angle,

So, Angle 3 = Angle 2

Similarly, Angle 4 and 106º are the pair of vertically opposite angle

So, Angle 4 = 106º

The sum of all angles at point is equal to 360º

So,

`\begin{gathered} \angle2+\angle3+\angle4+106=360 \\ \text{ Since},\text{ }\angle4=106\text{ and }\angle3=\angle2 \\ \angle2+\angle2+106+106=360 \\ 2\angle2+212=360 \\ 2\angle2=360-212 \\ 2\angle2=148 \\ \angle2=(148)/(2) \\ \angle2=74 \\ \text{ As, }\angle2=\angle3 \\ \angle3=74 \end{gathered}`

So, m<2 = 74º, m<3 = 74º, m<4 = 106º

Answer :

m<2 = 74º

m<3 = 74º

m<4 = 106º