Question

I need help in this it would be of great help

Answer 1

Answer:

The measure of angle b is;

$b=30^{\circ}$

Explanation:

Given the figure in the attached image.

line m and n are parallel lines.

To solve for angle b, let x represent the corresponding angle to angle 120 degree, as shown below;

So, angle x is equal to 120 degree.

$x=120^{\circ}$

Reason: corresponding angle.

Angle x is an exterior angle to the triangle alog the line n.

So, angle x equals the sum of angle b and 90 degree.

$\begin{gathered} x=b+90^{\circ} \\ b=x-90^{\circ} \end{gathered}$

Reason: Exterior angle theorem of a triangle.

substituting the value of x;

$\begin{gathered} b=x-90^{\circ} \\ b=120^{\circ}-90^{\circ} \\ b=30^{\circ} \end{gathered}$

Therefore, the measure of angle b is;

$b=30^{\circ}$