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Given that line AB is parallel to line CD, angle PTS = 65° as shown on the diagram below. (a) Find the value of y. (b) Calculate the size of angle marked m in degrees.

June 5, 2026Mathematics

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Step-by-step solution

3 steps

a) Find the value of $y$ .

Identify the properties of triangle SPT.
The markings on sides SP and PT indicate that $\triangle SPT$ is an isosceles triangle, meaning $SP = PT$ . In an isosceles triangle, the angles opposite the equal sides are equal.
Therefore, $\angle PST = \angle PTS$ .
Use the given angle to find $\angle PST$ .
Given $\angle PTS = 65^\circ$ .
So, $\angle PST = 65^\circ$ .
Set up an equation for $y$ .
The angle $\angle PST$ is given as $5y$ .
$5y = 65^\circ$