Question

M∠3=

a) 44
b) 88
c) 136

Answer 1

`\angle 4 = (1)/(2) (46 + 42)`


`\angle 4 = 44`


`\angle 1 = 180 - 44 = 136 \textdegree` . [ Adjacent angles on a straight line add up to 180° ]

Answer 2

`m\angle 3=136^(\circ)`

Explanation:

We are given that

Measure of intercepted arc are

`46^(\circ),42^(\circ)`

We have to find the measure of angle 3.

We know that

Internal angle=half the sum of measures of its intercepted arc.

Using this property

Measure of angle 4=
`(1)/(2)(46+42)=44^(\circ)`

Measure of angle 4 +measure pf angle 3=180 degrees (linear pair)

Substitute the values then we get

`44^(\circ)+m\angle 3=180^(\circ)`

`m\angle 3=180-44=136^(\circ)`

Hence, the
`m\angle 3=136^(\circ)`