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Side QR of a triangle PQR is produced both ways and the measures of exterior angles formed are 86° and 124°. The measure of ∠P is :
- a)30°
- b)40°
- c)60°
- d)80°
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Side QR of a triangle PQR is produced both ways and the measures of ex...
∠PQX and ∠PRY are exterior angles for ΔPQR
∴ ∠P + ∠PRY = 86° ...(i)
∠P + ∠PQX = 124° ...(ii)
Adding (i) and (ii)
2∠P +∠PRX + ∠PQX = 210°
⇒∠P + (∠P +∠PRX + ∠PQX) = 210°
⇒ ∠P + 180° = 210°
⇒ ∠P = 30°
∴ ∠P + ∠PRY = 86° ...(i)
∠P + ∠PQX = 124° ...(ii)
Adding (i) and (ii)
2∠P +∠PRX + ∠PQX = 210°
⇒∠P + (∠P +∠PRX + ∠PQX) = 210°
⇒ ∠P + 180° = 210°
⇒ ∠P = 30°
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Side QR of a triangle PQR is produced both ways and the measures of ex...
Understanding the Problem
In triangle PQR, side QR is extended both ways, creating two exterior angles: one measuring 86° and the other measuring 124°. We need to find the measure of angle P.
Properties of Exterior Angles
- Exterior angles of a triangle are formed when a side is extended.
- Each exterior angle is equal to the sum of the two opposite interior angles.
Calculating Angle Measures
1. Identify the angles:
- Let angle Q (interior) be denoted as angle Q.
- Let angle R (interior) be denoted as angle R.
- We know the exterior angles:
- Exterior angle at Q = 86°
- Exterior angle at R = 124°
2. Using the property of exterior angles:
- For exterior angle at Q:
- Exterior angle (86°) = angle P + angle R
- So, angle P + angle R = 86° (1)
- For exterior angle at R:
- Exterior angle (124°) = angle P + angle Q
- So, angle P + angle Q = 124° (2)
3. Adding equations (1) and (2):
- (angle P + angle R) + (angle P + angle Q) = 86° + 124°
- 2 * angle P + angle Q + angle R = 210°
4. Using the triangle sum property:
- angle P + angle Q + angle R = 180°
- Substitute angle Q + angle R = 180° - angle P into the previous equation.
5. Final Calculation:
- 2 * angle P + (180° - angle P) = 210°
- angle P = 30°
Conclusion
The measure of angle P is 30°, which corresponds to option 'A'.
In triangle PQR, side QR is extended both ways, creating two exterior angles: one measuring 86° and the other measuring 124°. We need to find the measure of angle P.
Properties of Exterior Angles
- Exterior angles of a triangle are formed when a side is extended.
- Each exterior angle is equal to the sum of the two opposite interior angles.
Calculating Angle Measures
1. Identify the angles:
- Let angle Q (interior) be denoted as angle Q.
- Let angle R (interior) be denoted as angle R.
- We know the exterior angles:
- Exterior angle at Q = 86°
- Exterior angle at R = 124°
2. Using the property of exterior angles:
- For exterior angle at Q:
- Exterior angle (86°) = angle P + angle R
- So, angle P + angle R = 86° (1)
- For exterior angle at R:
- Exterior angle (124°) = angle P + angle Q
- So, angle P + angle Q = 124° (2)
3. Adding equations (1) and (2):
- (angle P + angle R) + (angle P + angle Q) = 86° + 124°
- 2 * angle P + angle Q + angle R = 210°
4. Using the triangle sum property:
- angle P + angle Q + angle R = 180°
- Substitute angle Q + angle R = 180° - angle P into the previous equation.
5. Final Calculation:
- 2 * angle P + (180° - angle P) = 210°
- angle P = 30°
Conclusion
The measure of angle P is 30°, which corresponds to option 'A'.
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Side QR of a triangle PQR is produced both ways and the measures of exterior angles formed are 86° and 124°. The measure of ∠P is :a)30°b)40°c)60°d)80°Correct answer is option 'A'. Can you explain this answer?
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Side QR of a triangle PQR is produced both ways and the measures of exterior angles formed are 86° and 124°. The measure of ∠P is :a)30°b)40°c)60°d)80°Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Side QR of a triangle PQR is produced both ways and the measures of exterior angles formed are 86° and 124°. The measure of ∠P is :a)30°b)40°c)60°d)80°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Side QR of a triangle PQR is produced both ways and the measures of exterior angles formed are 86° and 124°. The measure of ∠P is :a)30°b)40°c)60°d)80°Correct answer is option 'A'. Can you explain this answer?.
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