Question

M∠3= a) 44 b) 88 c) 136

Answer 1

Answer:

$m\angle 3=136^{\circ}$

Step-by-step 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=$\frac{1}{2}(46+42)=44^{\circ}$

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 $m\angle 3=136^{\circ}$

Answer 2

$\angle 4 = \frac{1}{2} (46 + 42)$

$\angle 4 = 44$

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