Question

Find the values of the angles x, y and z in each of the following:

• A. $x={115}^{\circ },y={140}^{\circ }andz={40}^{\circ }$
• B. $x={175}^{\circ },y={120}^{\circ }andz={30}^{\circ }$
• C. $x={215}^{\circ },y={10}^{\circ }andz={40}^{\circ }$
• D. $x={125}^{\circ },y={190}^{\circ }andz={40}^{\circ }$

Answer 1

The correct option is A $x={115}^{\circ },y={140}^{\circ }andz={40}^{\circ }$

${40}^{\circ }+x+{25}^{\circ }={180}^{\circ }\text{[Angles on straight line]}\Rightarrow {65}^{\circ }+x=180\Rightarrow x={180}^{\circ }-{65}^{\circ }={115}^{\circ }Now,{40}^{\circ }+y={180}^{\circ }\text{[Linear pair]}\Rightarrow y={180}^{\circ }-{40}^{\circ }={140}^{\circ }....\left(i\right)Also{40}^{\circ }+y={180}^{\circ }\text{[Linear pair]}\Rightarrow {140}^{\circ }+z={180}^{\circ }\text{[From eq.(i)]}\Rightarrow z={180}^{\circ }-{140}^{\circ }={40}^{\circ }Thus,x={115}^{\circ },y={140}^{\circ }andz={40}^{\circ }$