Two chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31^o and ∠PKR = 42^o, find ∠KQR

Mrnoah

1 year ago

Since PQ and RS are chords of the circle, we can use the property that the angle subtended by a chord at the center of the circle is twice the angle subtended by the chord at any point on the circumference.

Given:

∠KPS = 31°
∠PKR = 42°

Since ∠KPS and ∠PKR are vertically opposite angles:

∠KPS = ∠PKR

However, we are given that ∠KPS = 31° and ∠PKR = 42°, which are not equal.

This implies that ∠KPS and ∠PKR are not vertically opposite angles, but rather, they are angles formed by the intersection of the chords PQ and RS.

Using the property that the angle subtended by a chord at the center of the circle is twice the angle subtended by the chord at any point on the circumference:

∠KQR = 180° - (∠KPS + ∠PKR)

Substituting the given values:

∠KQR = 180° - (31° + 42°)
= 180° - 73°
= 107°

Therefore, ∠KQR = 107°.