Question

(a) Find the value of angles 2,3,4 if $\angle$1 is 45. [4 MARKS]

(b) The supplement of which angle is the complement of ${70}^{\circ }$?

Answer 1

(a) Steps: 1 Mark
Angles: 1 Mark
(b) Steps: 1 Mark
Result: 1 Mark

(a) Given $\angle 1={45}^{\circ }$

$\Rightarrow \angle 3=\angle 1={45}^{\circ }$ [Vertically opposite angle]

$\angle 2+\angle 3={180}^{\circ }$ [Linear pair]

$\angle 2+\angle {45}^{\circ }={180}^{\circ }$

$\angle 2={180}^{\circ }-\angle {45}^{\circ }$

$\Rightarrow \angle 2={135}^{\circ }$

$\Rightarrow \angle 2=\angle 4$ [Vertically opposite angle]

$\Rightarrow \angle 4=\angle 2={135}^{\circ }$


(b) Let the angle be $x^{\circ }$

$\therefore$ its supplementary angle = $(180-x{)}^{\circ }$

Given that $(180-x{)}^{\circ }$ is the complementary angle of ${70}^{\circ }$

$\therefore (180-x)+70=90$

$\Rightarrow x=180-20$

$\Rightarrow x={160}^{\circ }$
The required angle is ${160}^{\circ }$.