Question

Match the following figures with their corresponding mathematical relation between the angles.

• A. 1+2+3=${180}^{\circ }$
• B. 1 = ${60}^{\circ }$
• C. 5+4= ${120}^{\circ }$

Answer 1

For the figure 1:
$\angle$1, $\angle$2 and $\angle$3 forms a linear pair, therefore $\angle$1 + $\angle$2 + $\angle$3 = ${180}^{\circ }$
For the figure 2:
$\angle$1, $\angle$BOC and $\angle$COE forms a linear pair,
therefore $\angle$1 +$\angle$BOC +$\angle$COE = ${180}^{\circ }$
Given : $\angle$BOC = ${30}^{\circ }$,$\angle$COE = ${90}^{\circ }$
$\Rightarrow$ $\angle$1 +$\angle$BOC +$\angle$COE = ${180}^{\circ }$
$\Rightarrow$ $\angle$1 + ${30}^{\circ }$ + ${90}^{\circ }$ = ${180}^{\circ }$
$\Rightarrow$ $\angle$1 = ${60}^{\circ }$
For the figure 3:
$\angle$4, $\angle$5 and $\angle$FOB forms a linear pair,
therefore $\angle$1 +$\angle$5 +$\angle$FOB = ${180}^{\circ }$
Given: $\angle$FOB = ${60}^{\circ }$
$\Rightarrow$ $\angle$4 + $\angle$5 + ${60}^{\circ }$ = ${180}^{\circ }$
$\Rightarrow$ $\angle$4 + $\angle$5 = ${120}^{\circ }$