This question involves finding the largest angle of a quadrilateral given the ratio of its angles.
Quadrilateral Angle Ratio Problem
The sum of the interior angles of any quadrilateral is always $360^\circ$. We are given that the angles are in the ratio 4 : 9 : 11 : 12.
Step-by-Step Solution
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Represent the angles:
Let the angles be $4x$, $9x$, $11x$, and $12x$, where $x$ is a common factor.
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Set up the equation:
The sum of these angles must equal $360^\circ$.
$4x + 9x + 11x + 12x = 360^\circ$
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Combine like terms:
Add the coefficients of $x$.
$(4 + 9 + 11 + 12)x = 360^\circ$
$36x = 360^\circ$
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Solve for $x$:
Divide both sides by 36.
$x = \frac{360^\circ}{36}$
$x = 10^\circ$
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Calculate the largest angle:
The largest angle corresponds to the largest part of the ratio, which is 12.
Largest angle = $12x = 12 \times 10^\circ = 120^\circ$.
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Conclusion:
The largest angle among the four angles is $120^\circ$.
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Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
