Answer:
Given : [tex]\overrightarrow{ST} \perp \overrightarrow{SR}[/tex]
Or we can say that A ray ST is perpendicular to Ray SR.
By the definition of Perpendicular lines: A perpendicular lines are lines that intersect at a right angle.
⇒ [tex]\angle RST[/tex] is right angle.
Then, by the definition of the right angle states that the angle bounded by the two perpendicular lines i.e, an angle of [tex]90^{\circ}[/tex].
⇒ [tex]\angle RST[/tex][tex]= 90^{\circ}[/tex]
Addition Angle theorems states that the sum of measure of two angle of an interior angle.
then, by the definition of the addition angle theorem we have ;
[tex]m\angle 1 +m\angle 2 = m\angle RST[/tex] ......[1]
Now, by substituting the value of [tex]\angle RST = 90^{\circ}[/tex] in above equation[1];
[tex]m\angle 1 +m\angle 2 =90^{\circ}[/tex] ......[2]
Subtraction property of Equality states that subtract the same number from both sides of an equation.
Now, subtract [tex]m\angle 2[/tex] from both sides of an equation [2];
[tex]m\angle 1 +m\angle 2 -m\angle 2 =90^{\circ}-m\angle 2[/tex]
On simplify we get,
[tex]m\angle 1 =90^{\circ} - m\angle 2[/tex] Hence proved!
The figure as you can see in the attachment.
