Question

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Answer 1

Step-by-step explanation:

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Answer 2

• ∠B is of 75°

Step-by-step explanation:

Given:-

• Quadrilateral ABCD is a cyclic quadrilateral.
• ∠B = ∠D - 30°

To find:-

• Value of ∠B

Solution:-

We know,

Sum of opposite angles of cyclic quadrilateral is 180°.

So,

$\longrightarrow$ ∠B + ∠D = 180°

• Put ∠B = ∠D - 30°

$\longrightarrow$ ∠D - 30° + ∠D = 180°

$\longrightarrow$ ∠D + ∠D = 180° + 30°

$\longrightarrow$ 2 ∠D = 210°

$\longrightarrow$ ∠D = 210°/2

$\longrightarrow$ ∠D = 105°

Now,

$\longrightarrow$ ∠B = ∠D - 30°

• Put ∠D = 105°

$\longrightarrow$ ∠B = 105° - 30°

$\longrightarrow \pink{\boxed{\sf \bold{\angle B = 75\degree}}\star}$

Verification:-

$\longrightarrow$ ∠B + ∠D = 180°

• Put ∠B = 75° and ∠D = 105°

$\longrightarrow$ 75° + 105° = 180°

$\longrightarrow$ 180° = 180°

$\boxed{\sf Hence \: Verified.}$

Therefore,

∠B is of 75°.