Question

Find the value of m angle 3-m<1

Answer 1

Answer:

The value of $m\angle 3-m\angle 1$ = $50^{\circ}$

Step-by-step explanation:

Vertical Angle theorem: It is about the angles that are opposite to each other.

Also, vertical angle are congruent that means vertical angles are equal.

In the given figure; $m\angle 3$ and $70^{\circ}$ are vertical angle

then, by vertical angle theorem,  $m\angle3 =70^{\circ}$.

Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.

From the figure, $70^{\circ}$ , $\angle 1$ and $m\angle 2 =90^{\circ}$ forms a straight line.

then, by the definition of Supplementary angle;

$70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}$

Substituting the value of  $m\angle 2 =90^{\circ}$ in above equation:

$70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}$ or

$160^{\circ}+m\angle 1=180^{\circ}$

Simplify:

$m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}$

therefore,  $m\angle 1= 20^{\circ}$ and $m\angle 3=70^{\circ}$,

the value of $m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}$.