In triangle PQR ∠ P: ∠ Q: ∠ R=3:2:1 and PQ║RD. Find measure of ∠ERD
Answers
Answer:
Step-by-step explanation:
angle P : angle Q : angle R = 3:2:1
angle P = 3x
angle Q = 2x
angle R = 1x
we all know that sum of interior angles of a triangle is 180°.
angle P + angle Q + angle R = 180°.
3x+2x+1x = 180°.
6x = 180°
x = 180/6
x = 30°.
angle P = 3x = 3 x 30° = 90°
angle Q = 2x = 2 x 30° = 60°
angle R = 1x = 1 x 30° = 30°
according to the given data of angles the figure will be like this given in the attachment below-REFER THE FIRST FIGURE FOR THE ANGLES!
now , to find angle ERD
As PQ // RD
[FOR PQ//RD - REFER THE SECOND FIGURE WHICH I HAVE GIVEN IN THE ATTACHMENT BELOW!
angle DRQ = angle PQR(alternate interior angles)
as angle PQR = 60°
angle DRQ = 60° [as angle DRQ = angle PQR]
angle PRQ = 30° [find above]
angle ERP = angle DRQ = 60° [ BECAUSE PQ // RD]
so angle PRQ = 30°
angle ERD(when it is not a straight line)
= angle PRQ + angle ERP + angle DRQ
= 30° + 60° + 60°
= 150°
so the measure of angle ERD = 150°
(which is not a straight line)
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