Find x in the given fig. 5.26. Class 9

Find x in the given fig. 5.26. Class 9

Question 1.

Find x in the given fig. 5.26. Class 9

Solution:

∠ADC = 100° ...[Given]

So, the arc intercepted by ∠ADC is the major arc AC.

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

∴ measure of major arc AC = 2 × 100° = 200° Then,

measure of minor arc AC = 360° - 200°

= 160°

Now, ∠ABC subtends the minor arc AC.

∴ x = ∠ABC = $\frac{1}{2}$ × 160°= 80°

Question 2.

Exercise: A cyclic quadrilateral has angles measuring ∠A = 80°, ∠B = 110°, ∠C = 100°, and ∠D = 70°. Can such a quadrilateral be drawn?

Explain why or why not. Class 9

Answer:

Yes, such a cyclic quadrilateral can be drawn. The sum of two opposite angles of a cyclic quadrilateral is 180°.

Here, ∠A + ∠C = 80° +100° = 180° and ∠B + ∠D = 110° + 70° = 180°

Since both pairs of opposite angles are supplementary, such a cyclic quadrilateral can be drawn.