Question

if ABCD is a cyclic quadrilateral in which ab parallel BC prove that angle b = angle C

Answer 1

Given: ABCD is a cyclic quadrilateral in which ab parallel c d.

To Prove : ∠ b=∠c

Proof: As we know sum of opposite angles of cyclic quadrilateral is Supplementary.

∠a + ∠c=180°-------(1)

∠b + ∠d = 180°------(2)

As , ab ║ c d

∠ a + ∠d= 180°-------(3)

∠b + ∠c= 180°--------(4)

Equating (1) and (3) and (1) and (4)

∠a + ∠c=∠ a + ∠d        

∠c=∠d→→Cancelling ∠ a from both sides

→→   ∠a + ∠c= ∠b + ∠d

As, ∠c=∠d

So, ∠a=∠b

Answer 2

Answer:

Step-by-step explanation:

Given: ABCD is a cyclic quadrilateral in which ab parallel c d.

To Prove : ∠B=∠C

Proof: As we know sum of opposite angles of cyclic quadrilateral is Supplementary.

∠A + ∠C=180°-------(1)

∠B + ∠D = 180°------(2)

As , AB ║ CD

∠A + ∠D= 180°-------(3)

∠B + ∠C= 180°--------(4)

Equating (1) and (3) and (1) and (4)

∠A + ∠C=∠ A + ∠D        

∠C=∠D→→Cancelling ∠ a from both sides

→→   ∠A + ∠C= ∠B+ ∠D

As, ∠C=∠D

So, ∠A=∠B

    Hence proved