The
angles of
a quadri lateral are in the ratio of 5:6:10:15. Find the angles of a quadrilateral
Answers
Answer:50,60,100,150
Step-by-step explanation:
5+6+10+15=36
360/36=10
5*10=50
6*10=60
10*10=100
15*10=150
Answer:
The angles of the quadrilateral are 50°, 60°, 100° and 150°.
Step-by-step-explanation:
We have given that,
The angles of a quadrilateral are in the ratio
5 : 6 : 10 : 15.
Let the common multiple be x.
We know that,
The sum of angles of a quadrilateral is 360°.
∴ 5x + 6x + 10x + 15x = 360°
⇒ 11x + 25x = 360°
⇒ 36x = 360
⇒ x = 360 ÷ 36
⇒ x = 10°
Now,
First angle = 5x
⇒ 5 × 10
⇒ First angle = 50°
Now,
Second angle = 6x
⇒ 6 × 10
⇒ Second angle = 60°
Now,
Third angle = 10x
⇒ 10 × 10
⇒ Third angle = 100°
Now,
Fourth angle = 15x
⇒ 15 × 10
⇒ Fourth angle = 150°
∴ The angles of the quadrilateral are 50°, 60°, 100° and 150°.
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Additional Information:
1. Quadrilateral:
A geometric figure formed by joining four line segments, two in a common point is called as a quadrilateral.
2. Property of Quadrilateral:
The sum of measures of all angles of a quadrilateral is 360°.
3. Types of Quadrilateral:
A. Parallelogram
B. Trapezium
C. Kite
4. Parallelogram:
A quadrilateral having its opposite sides parallel is called parallelogram.
5. Types of Parallelogram:
A. Rhombus
B. Rectangle
C. Square
6. Rhombus:
A parallelogram having its all sides of equal measures is called as rhombus.
7. Rectangle:
A parallelogram having its all angles right angles is called as a rectangle.
8. Square:
A parallelogram having its all sides of equal measures and all angles are right angles is called as square.
9. Trapezium:
A quadrilateral having one pair of its sides parallel is called as trapezium.
10. Kite:
A quadrilateral having opposite sides equal but both pairs of opposite sides are of different measures.