In the given figure, if PQ || RS, ∠𝑄𝑃𝑇 = 560 and ∠𝑇𝑅𝑆 = 140, thenfind the measure of angle m
Question
In the given figure, if PQ || RS,
- ∠𝑄𝑃𝑇 = 56°
- ∠𝑇𝑅𝑆 = 14°
then find the measure of angle m.
Solution
To find the measure of angle m, we can use the properties of parallel lines and transversal lines.
Since PQ || RS and PT is a transversal, we know that alternate interior angles are equal. So, ∠QPT = ∠TRS.
Given that ∠TRS = 140°, this means ∠QPT = 140°.
Now, we know that ∠QPT = ∠QPT + m (because m is part of ∠QPT).
So, we can set up the equation 140° = 56° + m to find the value of m.
Subtract 56° from both sides to solve for m:
140° - 56° = m 84° = m
So, the measure of angle m is 84°.
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