Question

In a kite ABCD, AB=AD, BC=CD; CAD=40° and

Answer 1

Answer: See below

Step-by-step explanation:

From the figure attached below,

We know that by the SSS property, the two triangles are congruent

$Since, \begin{aligned}&A D=A B(\text {Given}) \\&C D=B C(\text {Given}) \\&A C=A C \text { (Common side})\end{aligned} Hence, \triangle A B C \cong \triangle A C D By the properties of congruence, \angle O A D=\angle O A B=40^{\circ} \angle B=\angle D$

Using the property of congruence to find the measure of all these angles:

Therefore, the measure of the angles are:

$&a) \ B\widehat{ A} C=40^{\circ} \\ b) \ &B\widehat{C}A=180^{\circ}-\left(90^{\circ}+60^{\circ}\right)=30^{\circ} \\c) \ &A \widehat{D} C=60^{\circ}+50^{\circ}=110^{\circ}$