Question

Alice is a lady carpenter. She designed a fashionable circular table (as shown in fig below). She want to draw a design and plotted four points on the edge of the table. BD is the diameter of the table. Help her to find some measurements.

A) find he measure of angle A?
60°
90°
180°
30°

B) if DC is equal to BC, what is the measure of angle CBD?
60°
90°
45°
30°

C)sum of angles BCD and BAD?
60°
120°
180°
30°

D)what is the measure of angle ABD?
65°
115°
45°
35°

Answer 1

Answer:

(A) 90⁰

(B) 30⁰

(C) 180⁰

(D) 35⁰

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Answer 2

Given:

BD is the diameter

To find:

A. Angle A

B. Angle CBD

C. Sum of angles BCD and BAD

D. Angle ABD

Solution:

The required measure of angle A=90°, angle CBD=45°, BCD+BAD=180°, and angle ABD=65°.

We are given that the diameter is BD and ABCD is cyclic.

A. Since angle A is formed in the half-circle, it is 90 degrees.

Angle A=90°

B. Similarly, angle C is also equal to 90°.

Now, in ΔDCB,

angle C+angle CDB+angle CBD=180°

Also, DC=BC.

So, angle CDB=angle CBD

Using values,

90°+ 2(angle CBD)=180°

2(angle CBD)=90°

Angle CBD=45°

C. We already have that angle A and angle C are equal to 90°.

Angle BCD+angle BAD=angle A+angle C

=90°+90°

=180°

D. In ΔBAD, Angle A+angle ABD+angle ADB=180°

Using the values,

90°+angle ABD+25°=180°

Angle ABD=65°

Therefore, the required measure of angle A=90°, angle CBD=45°, BCD+BAD=180°, and angle ABD=65°.