Question

In the figure given below, O is the centre of the circle and AB is a diameter
IF AC=BD and AOC = 72. Find:
() ABC
(i) BAD
) ABD​

Answer 1

Answer:

ABC&BAD=72°

ABD=108°

Step-by-step explanation:

AOC=72°

ABC=AOC (opposite angles)

72°=72°

ABC+ABD=180°(linear pair)

or,ABD=180°-72°=108°

ABC=BAD (opposite angles)

72°=72°

Please mark me as brainliest.

Answer 2

Recall some properties of circle:

1. Angle at the centre of a circle is twice the angle at the circumference

2. In an isosceles trapezoid, the upper base angles are congruent. The lower base angles are also congruent.

3. Triangle inscribed in a semicircle is a right angle triangle.

4. Sum of the angles in a triangle is 180.

Find∠ABC:

$\text {Reason: Angle at the centre of the circle is twice the angle at the circumference}$

$\angle ABC = \angle AOC \div 2$

$\angle ABC = 72 \div 2$

$\angle ABC = 36$

Find∠BAD:

$\text{Reason: The upper base angles of an isosceles trapezoid are congruent }$

$\angle BAD = \angle ABC$

$\angle BAD = 36$

Find∠ABD:

$\text{Reason: triangle inscribed in a semicircle is a right angle triangle}$

$\angle ADB = 90$

$\text {Reason: Sum of angles in a triangle is 180}$

$\angle ABD = 180 - 90 - 36$

$\angle ABD = 54$