Question

Find $x+y+z+w$, in the given figure.

Answer 1

Since, the sum of the measures of interior angles of a quadrilateral is ${360}^{\circ }$

Also,${115}^{\circ }+{70}^{\circ }+{60}^{\circ }={245}^{\circ }$

$\therefore \angle ABC={360}^{\circ }-{245}^{\circ }={115}^{\circ }$

Now, $x=$ext$\angle BCD$

$={180}^{\circ }-{115}^{\circ }={65}^{\circ }$

$y={180}^{\circ }-{70}^{\circ }={110}^{\circ }$

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

$w={180}^{\circ }-{115}^{\circ }={65}^{\circ }$

$\therefore x+y+z+w={65}^{\circ }+{110}^{\circ }+{120}^{\circ }+{65}^{\circ }={360}^{\circ }$