pqrstu is a regular hexagon, determine each angle of PQT
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Answer:
Angle QPT=90, Angle PQT=60, and Angle PTQ=30. (All degrees).
Step-by-step explanation:
Given Problem:
PQRSTU is a regular hexagon. Determine each angle of triangle PQT.
Solution:
To Do:
Determine each angle of triangle PQT
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Method:
First of all we have to know:
★Properties Of Hexagon★
Angle tup = 120° degrees
TU = UP
According to your Question:
⇒The sum of interior angles of a polygon = (n – 2) × 180°
⇒The sum of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = 720°
⇒Measure of each angle of hexagon = \frac{720\°}{6} =120\°
∠PUT = 120° [Prove above]
In Δ PUT
∠PUT +∠UTP +∠TUP = 180° [angle sum property of a triangle]
120° + 2∠UTP = 180° [since ΔPUT is a isosceles triangle]
⇒2∠UTP = 180°- 120°
⇒∠UTP = \frac{60\°}{2} = 30\°
⇒∠UTP = ∠TPU = 30°
Similarly:
∠RTS = 30°
Therefore,
∠PTR = ∠UTS - ∠UTP - ∠RTS
∠PTR = 120° - 30° - 30° = 120° - 30° = 60°
∠TPQ = ∠UPQ - ∠UPT
∠TPQ = 120° - 30° = 90°
∠TPQ = 180° - 150° = 30°
[Using angle sum property of triangle in ΔPQT]