Question

In a quadrilateral with angles $A,B,C$ and $D$, if $m\angle A=m\angle B$ and $m\angle C$ is one half of $m\angle A$ while $m\angle D$ exceeds $\angle A$ by ${10}^o$, what are the values of $\angle A,\angle B,\angle C$ ad $\angle D$ respectively?

• A. $100,100,150,10$
• B. $75,75,150,60$
• C. $100,100,50,110$
• D. $90,90,45,100$
• E. $120,120,60,130$

Answer 1

The correct option is C $100,100,50,110$

Given: $m\angle A=m\angle B=x$(Let say 'x')

$m\angle C=\frac{x}{2}$, $m\angle D=x+{10}^o$

We know that the total sum of angles of a quadrilateral is $={360}^o$

so, $m\angle A+m\angle B+m\angle C+m\angle D={360}^o$

$x+x+\frac{x}{2}+x+10=360$

$3x+\frac{x}{2}=350$

$\frac{7x}{2}=350$

$\Rightarrow x=\frac{350\times 2}{7}=50\times 2$

$x={100}^o$

so, $m\angle A={100}^o=m\angle B$

$m\angle C=\frac{x}{2}=\frac{100}{2}={50}^o$

$m\angle D=x+{10}^o=100+10={110}^o$

$\Rightarrow$ Option 'C'.