Angle Sum Property of Quadrilateral
Angle Sum Property of Quadrilateral
The word quad means four and the word lateral means sides. Thus, a plane figure bounded by four line segments AB, BC, CD and DA is called a quadrilateral and is written as quad. ABCD or, ABCD. The points A, B, C, D are called its vertices. The four line segments, AB, BC, CD and DA are the four sides, and the four angles
,
,
and
are the four angles of quad. ABCD, Two line segments AC and BD are called the diagonals of quad. ABCD.
Theorem : The sum of the four angles of a quadrilateral is 360.
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GIVEN Quadrilateral ABCD To Prove <A + <B + <C + <D = 360 Construction Join BD Proof: In <1 + <2 + <3 = 180 .....(i) In <4 + <5 + <6 = 180 .......(ii) Adding (i) and (ii), we get <1 + <2 + <3 + <4 + <5 + <6 = 180 + 180 <1 + (<2 + <6 )+ <5+ (<3 + <4) = 180 + 180
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Illustration: In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2: 3 : 4. Find the measure of each angles of the quadrilateral.
Solution: We have, <A : <B : <C : <D = 1 : 2 : 3 : 4. So, let <A = x, <B = 2x, <C = 3x, < D = 4x.
<A + <B + <C + <D = 360
x + 2x + 3x + 4x = 360
10x = 360
x = 36
Thus, the angles are
The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral. | |||
| Right Option : B | |||
| View Explanation | |||
Find the value of x when other three angles are : 145, 66, 100 . | |||
| Right Option : A | |||
| View Explanation | |||
Find the value of x when other three angles are : 45, 60, 150 . | |||
| Right Option : B | |||
| View Explanation | |||
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