Question

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

CBD=60⁰ Calculate
(a) BAC angle
(b) BCA angle
(c) ADC angle​

Answer 1

Answer: See below

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)`