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Refer to the given diagram:

Note that, ﻿angle D B C equals 32 degree comma space angle A D B equals 22 degree comma space F i n d space angle A D C﻿





﻿36 degree﻿


﻿32 degree﻿


﻿54 degree﻿


﻿58 degree﻿



To solve the problem and find \( \angle ADC \), we can use the properties of cyclic quadrilaterals and angles within a circle.

### Given:
- \( \angle DBC = 32^\circ \)
- \( \angle ADB = 22^\circ \)

### Approach:
1. **Identify the cyclic quadrilateral**: Since points \( A \), \( B \), \( C \), and \( D \) lie on the circumference of the circle, the quadrilateral \( ABCD \) is cyclic. The opposite angles of a cyclic quadrilateral sum to \( 180^\circ \).

2. **Find \( \angle ABC \)**: We know that in cyclic quadrilaterals, opposite angles add up to \( 180^\circ \). Therefore, \( \angle ABC + \angle ADC = 180^\circ \).

3. **Use the angles given**: Consider triangle \( BCD \). The exterior angle of triangle \( BCD \), which is \( \angle ADB \), is equal to the sum of the opposite interior angles, i.e., \( \angle ABC \) and \( \angle BCD \).

Given that \( \angle DBC = 32^\circ \) and \( \angle ADB = 22^\circ \), we need to find \( \angle ADC \).

Let's calculate.

### Calculation:
We know that:

\[
\angle ABC + \angle ADC = 180^\circ
\]

Since \( \angle ABC = 180^\circ - \angle ADC \) and \( \angle ABC = 54^\circ \), it gives \( \angle ADC = 54^\circ \).

So the correct answer is \( 54^\circ \).

Would you like further details or explanations?

### 5 Relative Questions:
1. How do you calculate angles within a cyclic quadrilateral?
2. What is the significance of exterior angles in a circle?
3. How can you apply the opposite angle theorem in a cyclic quadrilateral?
4. Can you find \( \angle BCD \) based on other known angles in the diagram?
5. How does the central angle relate to the arc it subtends in a circle?

### Tip:
When dealing with cyclic quadrilaterals, remember that the opposite angles always sum up to \( 180^\circ \), which can be a powerful tool in solving related problems.

Refer to the given diagram: Note that, angle DBC = 32 degrees, angle ADB = 22 degrees. Find angle ADC.

In this problem, you will calculate the angle ADC in a cyclic quadrilateral. Given angles DBC = 32° and ADB = 22°, we will apply circle theorems to find the solution. This problem is ideal for students in Grades 9-11.

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