Question 14 Marks
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.
Answer
Sum of angles A, B, C and D of a quadrilateral = 360°
$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
But $\angle\text{A}=\angle\text{B}=\angle\text{C}=\angle\text{D}=1:2:4:5$
Let $\angle\text{A}=\text{x}$
Then $\angle\text{B}=2\text{x}$
$\angle\text{C}=4\text{x}$
$\angle\text{D}=5\text{x}$
$\text{x}+2\text{x}+4\text{x}+5\text{x}=360^\circ$
$\Rightarrow12\text{x}=360^\circ$
$\Rightarrow\text{x}=\frac{360}{12}=30^\circ$
$\angle\text{A}=\text{x}=30^\circ$
$\angle\text{B}=2\text{x}$
$=2\times30^\circ=60^\circ$
View full question & answer→Sum of angles A, B, C and D of a quadrilateral = 360°$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ$
But $\angle\text{A}=\angle\text{B}=\angle\text{C}=\angle\text{D}=1:2:4:5$
Let $\angle\text{A}=\text{x}$
Then $\angle\text{B}=2\text{x}$
$\angle\text{C}=4\text{x}$
$\angle\text{D}=5\text{x}$
$\text{x}+2\text{x}+4\text{x}+5\text{x}=360^\circ$
$\Rightarrow12\text{x}=360^\circ$
$\Rightarrow\text{x}=\frac{360}{12}=30^\circ$
$\angle\text{A}=\text{x}=30^\circ$
$\angle\text{B}=2\text{x}$
$=2\times30^\circ=60^\circ$
The sides of a quadrilateral ABCD are produced in order, forming exterior angles $\angle1$, $\angle2$, $\angle3$ and $\angle4$.