Question

Quadrilateral ABCD is shown if m

Answer 1

To begin, please note some of the properties of a kite;

The diagonals bisect each other at right angles (that is line BD and line AC meet at right angles)

The opposite angles where the unequal sides meet are equal in measure (that is angle ABC and angle ADC are equal in measure).

Therefore,

`\begin{gathered} In\text{ triangle EBC,} \\ \angle B=27,\angle E=90,\text{ hence} \\ \angle C=180-(27+90)\text{ angles in a triangle add up to 180} \\ \angle C=63 \end{gathered}`

Therefore, angle measure BCE = 63

Note also that triangle ABE is congruent to triangle ADE.

Hence, in triangle ABE, angle measure B equals angle measure D in triangle ADE. Therefore

`\begin{gathered} In\text{ triangle ABE,} \\ \angle B=52,\angle E=90,\text{ hence} \\ \angle A=180-(90+52) \\ \angle A=38 \end{gathered}`

Note also that the line AC is an angle bisector, since its perpendicular to line BD. That means angle measure BAE and DAE are equal in size.

Therefore, angle BAD

`\begin{gathered} \angle BAD=\angle BAE+\angle DAE \\ \angle BAD=38+38 \\ \angle BAD=76 \end{gathered}`