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)
[tex]\begin{gathered} m<1\text{ and 25}^0\text{ are linear pairs} \\ so\text{ they add up to 180}^0 \\ \end{gathered}[/tex]
This means that
[tex]\begin{gathered} m<1+25^0=180^0 \\ m<1=180^0-25^0 \\ m<1=155^0 \end{gathered}[/tex]
Thus, m<1 = 155°
To find the measure of angle 2 (m<2)
[tex]\begin{gathered} m<2\text{ and 25}^0\text{ are vertical angles} \\ \text{This means that they are equal} \end{gathered}[/tex]
Hence,
[tex]m<2=25^0[/tex]
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
[tex]m<3=90^0[/tex]
Thus,
m<3=90°
Hence, the summary of the solution is shown below
[tex]\begin{gathered} m\angle1\Rightarrow155^0 \\ m\angle2\Rightarrow25^0 \\ m\angle3\Rightarrow90^0 \end{gathered}[/tex]
