Question

Find the measures of $x$ , $y$ and $z$ in the figure, where $l\parallel BC$ .

• A. $\angle x={60}^0;\angle y={75}^0;\angle z={45}^0$
• B. $\angle x={30}^0;\angle y={75}^0;\angle z={75}^0$
• C. $\angle x={60}^0;\angle y={25}^0;\angle z={45}^0$
• D. None of these

Answer 1

Answer: (A)

Since, $l\parallel BC$, therefore,

$\angle ACB=z^{\circ }={45}^{\circ }$ [Pair of equal interior alternate angles]

$\angle ABC=y^{\circ }={75}^{\circ }$ [Pair of equal interior alternate angles]

Now, by Angle Sum Property, in $△ABC$

$\angle ACB+\angle ABC+\angle BAC={180}^{\circ }$

$z^{\circ }+y^{\circ }+x^{\circ }={180}^{\circ }$

${45}^{\circ }+{75}^{\circ }+x^{\circ }={180}^{\circ }$

$x^{\circ }={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Hence, option A. $\angle x={60}^{\circ };\angle y={75}^{\circ };\angle z={45}^{\circ }$ is correct.