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प्रश्न
In a quadrilateral the ratio of angles is 1 : 2 : 3 : 4. ∴ The largest angle is ______.
पर्याय
120°
150°
140°
144°
MCQ
रिकाम्या जागा भरा
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उत्तर
In a quadrilateral the ratio of angles is 1 : 2 : 3 : 4. ∴ The largest angle is 144°.
Explanation:
Step 1: Set up the equation
The sum of the interior angles of any quadrilateral is 360°. Given the ratio of the angles is 1 : 2 : 3 : 4, let the angles be represented as x, 2x, 3x and 4x. The sum of these angles must equal 360°.
x + 2x + 3x + 4x = 360°
Step 2: Solve for x
Combine the terms on the left side of the equation.
10x = 360°
Divide both sides by 10 to find the value of x.
`x = 360^circ/10 = 36^circ`
Step 3: Find the largest angle
The largest angle is represented by the largest ratio part, which is 4x. Substitute the value of x found in the previous step.
Largest angle = 4x = 4(36°) = 144°
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