Question

Figure the value of $x+y+z$ in Fig(i) and Fig (ii) respectively.

• A. ${225}^o,{320}^o$
• B. ${320}^o,{225}^o$
• C. ${320}^o,{215}^o$
• D. ${215}^o,{320}^o$

Answer 1

Answer: (C)

${320}^o,{215}^o$

Fir Fig(i), $AB||CD$

$\Rightarrow x={140}^o$ [Alternate interior angles]

$CD||EF$

$\Rightarrow y+z={180}^o$ [Co-interior angles]

Now, $x+y+z={140}^o+{180}^o={320}^o$

For Fig(ii), $CD||AB$

$\Rightarrow y={115}^o$ [Alternate interior angles]

$AD||BE$

$\to \angle DAB+\angle ABE={180}^o$ [Co-interior angles]

$\Rightarrow x+{30}^o+{115}^o={180}^o\Rightarrow x={35}^o$

$AB||EF$

$\Rightarrow \angle BEF=\angle ABE$ [Alternate interior angles]

$\Rightarrow z=x+{30}^o={35}^o+{30}^o={65}^o$

Now, $x+y+z={35}^o+{115}^o+{65}^o={215}^o$