Question

5. ABCD is a rhombus, APAB is equilateral,
D = 68°. Find the values of x and y.​

Answer 1

Answer:

x = 26° and y = 34°

Step-by-step explanation:

Given:- Triangle APB is equilateral and ABCD is a rhombus

also, angle D = 68°

To find:- x and y

Proof:-

We know that tri.APB is equilateral

thus, AP = PB = AB-------1

also, an.APB = an.PAB = an.PBA = 60°------2

NOTE: an. means angle for short, but dont use this in your notebooks I wrote this for simplicity

also ABCD is a rhombus

so, AB = BC = CD = AD------3

and opposite angles are equal

thus, an.ADC = an.ABC = 68°--------4

From eq.1 and eq.3 we get

AB = AP = PB = BC = CD = AD

Thus, PB = BC

then,

an.CPB = an.BCP = x (Properties of Isosceles Triangles)

so, x + y = 60°-------5

Now in Tri. PBC

From eq.2 and eq.4 we get

an.PBC = an.PBA + an.ABC

an.PBC = 60 + 68 = 128°

so, by Angle Sum Property we get

an.CPB + an.PBC + an.BCP = 180°

x + 128 + x = 180

2x = 180 - 128 = 52°

x = 52/2 = 26°

Now from eq.5 we get

26° + y = 60°

y = 60 - 26 = 34°

Hence, x = 26° and y = 34°

Hope you understood it........All the best