In Quadrilateral ABCD, + =140^ , : =1:3 and : =5:6. Find the valu… - Vidyadip

MCQ

In Quadrilateral ABCD, $\angle\text{A}+\angle\text{C}=140^\circ, \ \angle\text{A}:\angle\text{C}=1:3$ and $\angle\text{B}:\angle\text{D}=5:6.$ Find the values of $\angle\text{A}, \ \angle\text{B}, \ \angle\text{C}$ and $\angle\text{D}\ ?$

A
35º, 100º, 105º, 120º
B
100º, 102º, 120º, 10º
C
10º, 20º, 100º, 260º
D
90º, 90º, 100º, 80º

✓

Answer

35º, 100º, 105º, 120º
Solution:
Given $\angle\text{A}+ \angle\text{C}=140^\circ$
And $\angle\text{A}: \angle\text{C} = 1:3$
And $\angle\text{B}:\angle\text{D}=5:6$
$\Rightarrow\ \angle\text{A} = \frac{1}{4}×1400=35^\circ$
$\Rightarrow\ \angle\text{C} = \frac{3}{4}×1400=105^\circ$
Now according to angle sum property of quadrilateral,
$\angle\text{A} +\angle\text{B}+ \angle\text{C}+ \angle\text{D} = 360^\circ$
$\Rightarrow\ 350^\circ+\angle\text{B}+ 1050^\circ +\angle\text{D} = 360^\circ$
$\Rightarrow\ \angle\text{B}+\angle\text{D} = 360^\circ−140^\circ=220^\circ$
$\Rightarrow\ 5\text{x} + 6\text{x} = 220^\circ$
$\Rightarrow\ \text{x} = 20^\circ$
So, $\angle\text{B} = 5×20^\circ=100^\circ$
And $\angle\text{D}=6×20^\circ=120^\circ$

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