Advertisements
Advertisements
Question
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.
Advertisements
Solution
\[\text{ Let x be the measure of each angle } . \]
\[\text{ Then the ratio becomes x : 2x : 4x : 5x .} \]
\[ \text{ Since, the sum of all angles in a quadrilateral is } 360° , \text{ we have } : \]
\[x + 2x + 4x + 5x = 360° \]
\[ \Rightarrow 12x = 360° \]
\[ \Rightarrow x = \frac{360° }{12}\]
\[ \Rightarrow x = 30° \]
\[\text{ Thus, the angles are } : \]
\[x = 30 ° \]
\[2x = 60° \]
\[4x = 120° \]
\[5x = 150° \]
APPEARS IN
RELATED QUESTIONS
Define the following term Quadrilateral .
Complete of the following, so as to make a true statement:
A quadrilateral has ...... angles.
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
Complete the following statement by means of one of those given in brackets against each:
f consecutive sides of a parallelogram are equal, then it is necessarily a ..................
One diagonal of a rectangle is 18 cm. What is the length of its other diagonal?
One angle of a hexagon is 140° and the remaining angles are in the ratio 4 : 3 : 4 : 5 : 4. Calculate the measures of the smallest and the largest angles.
In a pentagon ABCDE, AB || ED and ∠B = 140°, ∠C = 2x° and ∠D = 3x°. Find ∠C and ∠D
In the quadrilateral ABCD, AB = BC and AD = DC Measure of ∠BCD is
In the following figure, name any two angles that appear to be obtuse angles.
In the following figure, What is AE + EC?
