Question

Find the value of m angle 3-m<1

Answer 1

The value of
`m\angle 3-m\angle 1` =
`50^(\circ)`

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)`.