Question

From the adjoining figure, calculate the value of a, b and c.

• A. $a={38}^{\circ },b={52}^{\circ }$ and $c={38}^{\circ }$
• B. $a={48}^{\circ },b={42}^{\circ }$ and $c={38}^{\circ }$
• C. $a={36}^{\circ },b={52}^{\circ }$ and $c={40}^{\circ }$
• D. $a={39}^{\circ },b={51}^{\circ }$ and $c={38}^{\circ }$

Answer 1

The correct option is A $a={38}^{\circ },b={52}^{\circ }$ and $c={38}^{\circ }$

Sum of all angles of a triangle $={180}^o$
$\therefore a+{110}^o+{32}^o={180}^o$
$\therefore a={38}^{\circ }$
Now, $a+b+{90}^o={180}^o$ (Sum of angles between parallel sides = 180^o)
$b+{38}^o+{90}^o={180}^o$
$b={52}^{\circ }$
Sum of all angles of a quadrilateral $={360}^o$
$\therefore a+b+{90}^o+{110}^o+{32}^o+c={360}^o$
${38}^o+{52}^o+{90}^o+{110}^o+{32}^o+c={360}^o$
$c+{322}^o={360}^o$
$c={38}^{\circ }$