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The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ?
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The bisector of angle A and angle B of a quadrilateral ABCD meet at P ...
Understanding the Quadrilateral ABCD
To analyze the angles in quadrilateral ABCD with angle A = angle B, angle C = 60°, and angle D = 110°, we can utilize the properties of angles in a polygon.
Sum of Angles in a Quadrilateral
- The sum of the interior angles of any quadrilateral is always 360°.
- Therefore, we can express this mathematically as:
Angle A + Angle B + Angle C + Angle D = 360°
Substituting Known Values
- Given that:
- Angle A = Angle B (let's denote them as x)
- Angle C = 60°
- Angle D = 110°
- We can substitute these values into the equation:
x + x + 60 + 110 = 360
Simplifying the Equation
- Combine like terms:
2x + 170 = 360
- Now, isolate 2x:
2x = 360 - 170
2x = 190
Finding Angle A and Angle B
- Divide by 2 to find x:
x = 190 / 2
x = 95°
- Therefore, Angle A = 95° and Angle B = 95°.
Conclusion
- In summary, for quadrilateral ABCD:
- Angle A = 95°
- Angle B = 95°
- Angle C = 60°
- Angle D = 110°
This analysis confirms that the angle properties hold true, maintaining the total of 360° for the quadrilateral.
To analyze the angles in quadrilateral ABCD with angle A = angle B, angle C = 60°, and angle D = 110°, we can utilize the properties of angles in a polygon.
Sum of Angles in a Quadrilateral
- The sum of the interior angles of any quadrilateral is always 360°.
- Therefore, we can express this mathematically as:
Angle A + Angle B + Angle C + Angle D = 360°
Substituting Known Values
- Given that:
- Angle A = Angle B (let's denote them as x)
- Angle C = 60°
- Angle D = 110°
- We can substitute these values into the equation:
x + x + 60 + 110 = 360
Simplifying the Equation
- Combine like terms:
2x + 170 = 360
- Now, isolate 2x:
2x = 360 - 170
2x = 190
Finding Angle A and Angle B
- Divide by 2 to find x:
x = 190 / 2
x = 95°
- Therefore, Angle A = 95° and Angle B = 95°.
Conclusion
- In summary, for quadrilateral ABCD:
- Angle A = 95°
- Angle B = 95°
- Angle C = 60°
- Angle D = 110°
This analysis confirms that the angle properties hold true, maintaining the total of 360° for the quadrilateral.
Community Answer
The bisector of angle A and angle B of a quadrilateral ABCD meet at P ...
Angle A- 95
Angle B- 95
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The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ?
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The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ?.
The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bisector of angle A and angle B of a quadrilateral ABCD meet at P .Determine angle A=angle B, angle C =60 and angle D = 110 ?.
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