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in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ
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in figure sides QP and RQ of angle PQR are produce to point S and T re...
Given information:
- Angle SPR = 135°
- Angle PQT = 110°
To find:
- Angle PRQ
Solution:
1. Understanding the problem:
- In the given figure, we have a triangle PQR.
- Sides QP and RQ are produced to points S and T, respectively.
- We need to find angle PRQ.
2. Analyzing the angles:
- We are given that angle SPR = 135° and angle PQT = 110°.
- From the given angles, we can identify two pairs of vertical angles:
- Angle SPR and angle QPS
- Angle PQT and angle RQT
3. Using vertical angles:
- Vertical angles are always equal, which means that angle SPR = angle QPS, and angle PQT = angle RQT.
- Therefore, we can conclude that angle QPS is also equal to 135° and angle RQT is equal to 110°.
4. Finding angle PRQ:
- We know that the sum of the angles in a triangle is equal to 180°.
- In triangle PQR, we have angle RPQ, angle PQR, and angle PRQ.
- We can calculate angle PRQ by subtracting the sum of angle RPQ and angle PQR from 180°.
- Let's assume angle RPQ = x and angle PQR = y.
5. Calculating angle PRQ:
- From the given information, we know that angle SPR = 135° and angle QPS = 135°.
- So, angle RPQ + angle QPS = angle SPR
- Substituting the values, we have x + 135° = 135°
- Simplifying the equation, we get x = 0°.
- Similarly, from the given information, we know that angle PQT = 110° and angle RQT = 110°.
- So, angle PQR + angle RQT = angle PQT
- Substituting the values, we have y + 110° = 110°
- Simplifying the equation, we get y = 0°.
- Now, we can calculate angle PRQ using the formula: angle PRQ = 180° - angle RPQ - angle PQR
- Substituting the values, we have angle PRQ = 180° - 0° - 0°
- Simplifying, we find angle PRQ = 180°.
6. Conclusion:
- After analyzing the given information and applying the concept of vertical angles, we found that angle PRQ is equal to 180°.
- Angle SPR = 135°
- Angle PQT = 110°
To find:
- Angle PRQ
Solution:
1. Understanding the problem:
- In the given figure, we have a triangle PQR.
- Sides QP and RQ are produced to points S and T, respectively.
- We need to find angle PRQ.
2. Analyzing the angles:
- We are given that angle SPR = 135° and angle PQT = 110°.
- From the given angles, we can identify two pairs of vertical angles:
- Angle SPR and angle QPS
- Angle PQT and angle RQT
3. Using vertical angles:
- Vertical angles are always equal, which means that angle SPR = angle QPS, and angle PQT = angle RQT.
- Therefore, we can conclude that angle QPS is also equal to 135° and angle RQT is equal to 110°.
4. Finding angle PRQ:
- We know that the sum of the angles in a triangle is equal to 180°.
- In triangle PQR, we have angle RPQ, angle PQR, and angle PRQ.
- We can calculate angle PRQ by subtracting the sum of angle RPQ and angle PQR from 180°.
- Let's assume angle RPQ = x and angle PQR = y.
5. Calculating angle PRQ:
- From the given information, we know that angle SPR = 135° and angle QPS = 135°.
- So, angle RPQ + angle QPS = angle SPR
- Substituting the values, we have x + 135° = 135°
- Simplifying the equation, we get x = 0°.
- Similarly, from the given information, we know that angle PQT = 110° and angle RQT = 110°.
- So, angle PQR + angle RQT = angle PQT
- Substituting the values, we have y + 110° = 110°
- Simplifying the equation, we get y = 0°.
- Now, we can calculate angle PRQ using the formula: angle PRQ = 180° - angle RPQ - angle PQR
- Substituting the values, we have angle PRQ = 180° - 0° - 0°
- Simplifying, we find angle PRQ = 180°.
6. Conclusion:
- After analyzing the given information and applying the concept of vertical angles, we found that angle PRQ is equal to 180°.
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in figure sides QP and RQ of angle PQR are produce to point S and T re...
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in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ
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in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ 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 in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ.
in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ 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 in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure sides QP and RQ of angle PQR are produce to point S and T respectively if angle SPR=135 AND ANGLE PQT=110 FIND ANGLE PRQ.
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