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Angle Sum Property of a Quadrilateral - Quadrilaterals, Class 9, Mathematics PDF Download

ANGLE SUM PROPERTY OF A QUADRILATERAL

THEOREM-I : The sum of the four angles of a quadrilateral is 360°.
Given : A quadrilateral ABCD.
To Prove : NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9A + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9B + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9C + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9D = 360°
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9
Construction : Join AC. 2 1
Proof :

STATEMENT REASON

1. In ΔABC
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 91+ NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 94+ 6 = 180°

2. In ΔADC
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 92 + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 93 + 5 =

3. (NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 91 +NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 92) + (NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 93 +NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 94) NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 95 +NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 96 = 180° + 180°

4. NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9A + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9C + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9D + B = 360°

5. NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9A + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9B + NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9C +NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9D = 360°

Sum of the all angles of triangle is equal to 180°

 

180° Sum of the all angles of triangle is equal to 180°

 

Adding (1) & (2), we get

 

 

Hence, proved.

Ex.1 Three angles of a quadrilateral measure 56°, 100° and 88°. Find the measure of the fourth angle.
Sol. Let the measure of the fourth angle be x°.
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 56° + 100° + 88° + x° = 360° NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 [Sum of all the angles of quadrileteral is 360°]
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 244+x=360
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 x = 360 – 244 = 116
Hence, the measure of the fourth angle is 116°.

Ex.2 The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
Sol. Let the four angles of the quadrilateral be 3x, 5x, 9x and 13x . [NCERT]
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 3x + 5x + 9x + 13x = 360° NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9[Sum of all the angles of quadrileteral is 360°]
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 30x = 360°
NCRT,Question and Answer,Important,Class 9 Mathematics,CBSE Class 9 x =12°
Hence, the angles of the quadrilateral are 3 × 12° = 36°, 5 × 12° = 60°, 9 × 12° = 108
The document Angle Sum Property of a Quadrilateral - Quadrilaterals, Class 9, Mathematics is a part of Class 9 category.
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FAQs on Angle Sum Property of a Quadrilateral - Quadrilaterals, Class 9, Mathematics

1. What is the Angle Sum Property of a Quadrilateral?
Ans. The Angle Sum Property of a Quadrilateral states that the sum of the four angles in any quadrilateral is always equal to 360 degrees.
2. How can I prove the Angle Sum Property of a Quadrilateral?
Ans. The Angle Sum Property of a Quadrilateral can be proven by dividing the quadrilateral into two triangles. By using the fact that the sum of the angles in a triangle is always 180 degrees, you can show that the sum of the four angles in a quadrilateral is indeed 360 degrees.
3. Can the angles in a quadrilateral be unequal?
Ans. Yes, the angles in a quadrilateral can be unequal. The only requirement is that the sum of the four angles must always be 360 degrees. This means that the angles can vary in size, as long as their sum remains constant.
4. Is the Angle Sum Property applicable to all quadrilaterals?
Ans. Yes, the Angle Sum Property is applicable to all quadrilaterals. It holds true for all types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, and rhombuses.
5. Can the Angle Sum Property be extended to polygons with more than four sides?
Ans. No, the Angle Sum Property is specific to quadrilaterals and does not apply to polygons with more than four sides. The sum of the interior angles of a polygon with "n" sides can be calculated using the formula (n-2) × 180 degrees.
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