Question

CA=CD=BD,ANGLE DBC=35 AND ANGLE DCA=X FIND THE X VALUE

Answer 1

Answer:

Step-by-step explanation:

Solution:-

Given : AC = BC, angle DCA = angle ECB and angle DBC = angle EAC

∠ DCA = ∠ ECB (Given)

Adding ∠ ECD to both sides, we get

∠ DCA + ∠ ECD = ∠ ECB + ∠ ECD

Addition property

∠ ECA = ∠ DCB.

AC = BC (Given)

∠ DBC = ∠ EAC (Given)

⇒ Δ DBC ≡ Δ EAC  (By ASA postulate)

So, DC = EC          (By CPCT)

Hence proved.

Answer 2

Answer:

VALUE OF X° = 40°

Step-by-step explanation:

Given,

CA = CD = BD

angle DBC = 35°

angle DCA = x°

To find,

value of x°

Solution:

angle CBD = angle BCD = 35°

angle BDC = [180 - ( 35 + 35 ) ] °

= ( 180 - 70 ) °

= 110°

angle CAD = ( 180 - 110 )° { linear pairs }

= 70°

angle CAD = angle CDA = 70°

angle DAC = [ 180 - ( 70 + 70 ) ] °

= (180 - 140 )°

= 40°