Question

In the figure, if AB = AC and AD || BC, then x, y and z are respectively = _____.

• A. $x={70}^{\circ },y={70}^{\circ },z={55}^{\circ }$
• B. $x={70}^{\circ },y={55}^{\circ },z={55}^{\circ }$
• C. $x={55}^{\circ },y={55}^{\circ },z={55}^{\circ }$
• D. $x={70}^{\circ },y={55}^{\circ },z={70}^{\circ }$

Answer 1

The correct option is B

$x={70}^{\circ },y={55}^{\circ },z={55}^{\circ }$

AB || BC ..... (given)

z = $\angle EAD$ = 55° ...... (corresponding abgles)

AB = AC ..... (given)

y = z = 55° ............ (base angles of an isosceles triangle)

In $△$ABC, x + y + z = 180° ..... (sum of angles of a triangle)

x = 180° - 55° - 55°

x = 70°