Question

4. In each of the following figures, find the value of x ​

Answer 1

Answer:

x=40

Step-by-step explanation:

Given,

AD=BD=DC

∠ABD=50

∠DAC=x=??

In ΔABD,

∠ABD=∠DAB=50{∵Base angles of isoscele Δ are equal}

∠ABD+∠DAB+∠BDA =180 {∵Sum of interior angles of a Δ is 180}

or, 50 + 50 + ∠BDA = 180

or, ∠BDA = 180 - 100

∴∠BDA = 80

Again,

In ΔADC,

∠DAC=∠DCA=x{∵Base angles of isosceles Δ are equal}

∠DAC + ∠DCA = ∠BDA{∵Exterior angle equals to sum of two opposite interior angles of a triangle}

or, x + x = 80

or, 2x = 80

∴x = 40