In Quadrilateral ABCD, + =140^ , : =1:3 and : =5:6. Find the values of , , and ?

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

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 $\angle\text{D}\ ?$

✓
$35^\circ , 100^\circ , 105^\circ , 120^\circ$
B
$100^\circ , 102^\circ , 120^\circ , 10^\circ$
C
$10^\circ , 20^\circ , 100^\circ , 260^\circ$
D
$90^\circ , 90^\circ , 100^\circ , 80^\circ$

✓

Answer

Correct option: A.

$35^\circ , 100^\circ , 105^\circ , 120^\circ$

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 $\angle\text{D}=6×20^\circ=120^\circ$