Angle Sum Property of a Polygon
Trending Questions
Q.
What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Q. The angles of a quadrilateral are in the ratio 3:4:5:6. The largest angle of the quadrilateral is:
- 80°
- 100°
- 120°
- 140°
Q. The sum of interior angles a convex polygon having 'n' sides is equal to .
- n ×180°
- (n-2) × 180°
- (n-3) × 180°
- (n-4) × 180°
Q.
In the given figure, x = ?
25∘
35∘
45∘
55∘
Q. Question 3
In the given figure, If AB||CD, EF⊥CD and ∠GED=126∘, find ∠AGE, ∠GEF and ∠FGE.
![](https://search-static.byjusweb.com/question-images/byjus/_c6dce53cbd99ed5cbc990ea0fb23f819011cb39e20160920-1295-137gvuy.png)
In the given figure, If AB||CD, EF⊥CD and ∠GED=126∘, find ∠AGE, ∠GEF and ∠FGE.
![](https://search-static.byjusweb.com/question-images/byjus/_c6dce53cbd99ed5cbc990ea0fb23f819011cb39e20160920-1295-137gvuy.png)
Q. The measure of the angles of a quadrilateral ABCD are respectively in the ratio 1:2:3:4. Then which of the following is true
- AC=BD
- AD∥BC
- AB∥DC
- none of these
Q. Question 6
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Q. M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1460496/original_9th__maths___5th_quest____BLC.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1460496/original_9th__maths___5th_quest____BLC.png)
Q. Question 1
The angle of quadrilateral are in the ratio 3 : 5 : 9 :13. Find the all the angles of the quadrilateral.
The angle of quadrilateral are in the ratio 3 : 5 : 9 :13. Find the all the angles of the quadrilateral.
Q. ΔBUG is an isosceles triangle with BU = GU. Find all the angles.
![Image result for isosceles triangle questions](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/473671/original_Annotationtgfhy.png)
![Image result for isosceles triangle questions](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/473671/original_Annotationtgfhy.png)
- 50∘, 50∘, 80∘
- 45∘, 45∘, 90∘
- 42∘, 42∘, 96∘
- 60∘, 30∘, 90∘
Q. The measure of each exterior angle of a regular polygon of 15 sides is:
- 24 degrees
- 156 degrees
- 360 degrees
- 280 degrees
Q. Which of the following pair of angles are alternate exterior angles in the given figure?
![](data:image/png;base64, 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)
- ∠PXA and ∠QYD
- ∠YXB and ∠XYC
- ∠QYD and ∠QXA
- ∠YXB and ∠PXA
Q. The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.
Q.
AB = 8.5cm = Dc, BC = 8.5cm = DA
AB = 9.5cm = DC, BC = 5.5 cm = DA
AB = BC = DC = DA = 9.5cm
AB = 6.7 cm = BC, DC = DA = 5.7cm
Q. In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/908203/original_Slide_No._53_question.png)
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/908203/original_Slide_No._53_question.png)
- OA=12CD
- AP=12BC
- OB=12BD
- PD=AP
Q. Find the value of PQ if PM:MQ = 2:3.
- 5 cm
- 8 cm
- 16 cm
- 20 cm
Q. In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/908203/original_Slide_No._53_question.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/908203/original_Slide_No._53_question.png)
Q. If in a kite ABCD, AB = 3 cm and BC = 5 cm, then find the value of AD + CD.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/908142/original_Slide_No._51_question.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/908142/original_Slide_No._51_question.png)
- 3 cm
- 5 cm
- 8 cm
- 10 cm
Q. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Q. If the angles of a quadrilateral are in the ratio 3:4:5:6, then find the angles of the quadrilateral.
- 60∘, 80∘, 100∘, 120∘
- 120∘, 100∘, 80∘, 60∘
- 120∘, 60∘, 80∘, 100∘
- 80∘, 100∘, 120∘, 60∘
Q. The measures of five angles of a hexagon are equal and the sixth measure 1000. Then the measure of each of the five angle is
- 1300
- 1200
- 1240
- 1280
Q. Two angles are complementary. If the larger angle is twice the measure of a smaller angle, then smaller is _____
- 30∘
- 45∘
- 60∘
- 15∘
Q. In the figure, if ∠A+∠B+∠C+∠D+∠E+∠F=k× right angle, then k is :
![84171_2dc17cfe585a451fb0720a5ab1cf0521.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/84171_2dc17cfe585a451fb0720a5ab1cf0521.png)
![84171_2dc17cfe585a451fb0720a5ab1cf0521.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/84171_2dc17cfe585a451fb0720a5ab1cf0521.png)
- 2
- 3
- 4
- 5
Q. A quadrilateral has there acute angles, what will be the type of the fourth angle?
- Acute
- Obtuse
- Right
- None
Q. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_b59230252b68eb4299fafb91f8963d52df4a23de20160919-22781-1jdpun1.png)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_b59230252b68eb4299fafb91f8963d52df4a23de20160919-22781-1jdpun1.png)
Q. The angles of a quadrilateral are x∘, (x−10)∘, (x+30)∘ and (2x)∘. Find the value of the greatest angle. (2 marks)
Q. An angle is 34o less than its supplement. The measure of the angle is
- 148o
- None of these
- 37o
- 74o
Q.
The complementary angle of an angle is greater than twice of it by 21°. Find the measure of the angle.
- 27°
- 29°
- 21°
- 23°
Q.
The angles of a quadrilateral are in the ratio 1:2:3:4. Find all the angles of the quadrilateral. [3 MARKS]
Q. Which of the following pair of angles are alternate exterior angles in the given figure?
![](data:image/png;base64, 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)
- ∠PXA and ∠QYD
- ∠QYD and ∠QXA
- ∠YXB and ∠XYC
- ∠YXB and ∠PXA