ABC is an isosceles triangle such that AB AC, ∠ABC 55°, and AD is the median to the base BC. Find the measure of ∠BAD.

35^o

Concept Used

The median of an isosceles triangle is perpendicular bisector of the unequal opposite side and also an angle bisector.

Calculations

In given \(\Delta \)ABC, \(\angle\)ABC and \(\angle\)ACB are \({55}^\circ\)

Using angle sum property of the triangle

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

\(\angle\)BAC + \({55}^\circ\) +\({55}^\circ\) = \({180}^\circ\)

\(\angle\)BAC = \({70}^\circ\)

Using concept, we get

\(\angle\)BAD = \(\angle\)DAC

\(\angle\)BAD + \(\angle\)DAC = \(\angle\)BAC

2\(\angle\)BAD = \(\angle\)BAC

2\(\angle\)BAD = \({70}^\circ\)

\(\angle\)BAD = \({35}^\circ\)

Therefore, \(\angle\)BAD is \({35}^\circ\).