Question

Find the angles using the diagram below. Line ris // to lines, and line tis I toline s.S3225045tm21= 2m22= 4m3= 5

Answer 1

To begin answering the question, let us familiarize ourselves with some basic terms

Linear Pairs: Two adjacent angles are a linear pair when their noncommon sides are opposite rays.

If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees.

Vertical angles: Vertical angles are a pair of opposite angles formed by intersecting lines.

Vertical angles are equal.

We can now apply this knowledege to find the required angles

To find the measure of angle 1 (m<1)

`\begin{gathered} m<1\text{ and 25}^0\text{ are linear pairs} \\ so\text{ they add up to 180}^0 \\ \end{gathered}`

This means that

`\begin{gathered} m<1+25^0=180^0 \\ m<1=180^0-25^0 \\ m<1=155^0 \end{gathered}`

Thus, m<1 = 155°

To find the measure of angle 2 (m<2)

`\begin{gathered} m<2\text{ and 25}^0\text{ are vertical angles} \\ \text{This means that they are equal} \end{gathered}`

Hence,

`m<2=25^0`

m<2 =25°

To get the measure of angle 3 (m<3)

Given: Line t is perpendicular to s

Wehen two lines are perpendicular to eachother, they meet at right angle

This means that

`m<3=90^0`

Thus,

m<3=90°

Hence, the summary of the solution is shown below

`\begin{gathered} m\angle1\Rightarrow155^0 \\ m\angle2\Rightarrow25^0 \\ m\angle3\Rightarrow90^0 \end{gathered}`