The angles of a quadrilateral are in the ratio 2:3:6:7. Find the largest angle of the Quadrilateral.
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The angles of a quadrilateral are given as in the ratio 2:3:6:7
Let the angles be 2x, 3x, 6x, 7x.
The sum of angles of a quadrilateral = 360°
⇒2x+3x+6x+7x = 360
⇒18x = 360
⇒x = 360/18
∴x = 20
∴The largest angle = 7x = 7×20 =140°
Let the angles be 2x, 3x, 6x, 7x.
The sum of angles of a quadrilateral = 360°
⇒2x+3x+6x+7x = 360
⇒18x = 360
⇒x = 360/18
∴x = 20
∴The largest angle = 7x = 7×20 =140°
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The largest angle of the Quadrilateral is 140° if angles of a quadrilateral are in the ratio 2:3:6:7
Given:
- Angles of a quadrilateral are in the ratio 2:3:6:7
To Find:
- The largest angle of the Quadrilateral.
Solution:
- Sum of all the angles of a quadrilateral is 360°
Step 1:
Assume that angles are:
2x, 3x ,6x and 7x
Step 2:
Add all the angles and equate with 360°
2x + 3x + 6x + 7x = 360°
Step 3:
Solve for x:
18x = 360°
=> x = 20°
Step 4 :
Substitute x = 20° in each angle
2x = 2 * 20° = 40°
3x = 3 * 20° = 60°
6x = 6 * 20° = 120°
7x = 7 * 20° = 140°
Step 5 :
Identify the largest angle
140°
The largest angle of the Quadrilateral is 140°
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