Question

please help me with this qn

Answer 1

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For finding x and y, we can use some theorams related to circles. From which, we can easily find the values.

Finding y:

Angle AOB is the angle subtended on the centre of the circle. And Angle ACB is somewhere on the circle.

We know that,

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

⇛ Angle ACB = 1/2 × Angle AOB

⇛ Angle ACB = 1/2 × 110°

⇛ Angle ACB = 55°

Thus, Angle y which is same as Angle ACB is equals to 55°

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Finding x:

Now in ∆ACD, AD is the diameter, so the angle subtended by the semi-circle is Angle ACD.

We know that, The inscribed angle is formed by drawing a line from each end of the diameter to any point on the semicircle. No matter where you do this, the angle formed is always 90°.

⇛ Angle ACD = 90°

⇛ x + y = 90°

Plugging the value of y

⇛ x + 55° = 90°

⇛ x = 35°

Thus the measure of the angle x is equals to 35°. And we are done...

Answer 2

Answer:

For finding x and y, we can use some theorams related to circles. From which, we can easily find the values.

Finding y:

Angle AOB is the angle subtended on the centre of the circle. And Angle ACB is somewhere on the circle.

We know that,

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

⇛ Angle ACB = 1/2 × Angle AOB

⇛ Angle ACB = 1/2 × 110°

⇛ Angle ACB = 55°

Thus, Angle y which is same as Angle ACB is equals to 55°

━━━━━━━━━━━━━━━━━━━━

Finding x:

Now in ∆ACD, AD is the diameter, so the angle subtended by the semi-circle is Angle ACD.

We know that, The inscribed angle is formed by drawing a line from each end of the diameter to any point on the semicircle. No matter where you do this, the angle formed is always 90°.

⇛ Angle ACD = 90°

⇛ x + y = 90°

Plugging the value of y

⇛ x + 55° = 90°

⇛ x = 35°

Thus the measure of the angle x is equals to 35°. And we are done...