chords PQ And RS Intersect At X Inside The Circle Centre T.If Angle PTR=64 Degree And The Minor Arc PR Is Twice The Minor Arc QS.Calculate QXS
Ans is 5
To calculate the value of angle QXS, we need to use the information given in the problem.
Let's analyze the information step by step:
1. We are given that chords PQ and RS intersect at point X inside the circle with center T.
2. The measure of angle PTR is 64 degrees.
Based on this information, we can begin by drawing a diagram. Let's draw a circle with center T and label points P, Q, R, and S on the circumference. The chords PQ and RS intersect at point X inside the circle.
Now, let's focus on the information related to the minor arcs:
3. The problem states that the measure of minor arc PR is twice the measure of minor arc QS.
Since we know that the measure of an angle formed by two intersecting chords is half the sum of the measures of the arcs intercepted by the angle, we can use this information to find the measure of angle QXS.
4. Let's consider the angle QXS and the associated arcs.
The angle QXS intercepts two arcs, namely minor arc QS and minor arc XR.
5. We have to compare the measures of these two arcs.
Given that the measure of minor arc PR is twice the measure of minor arc QS, we can conclude that the measure of minor arc QR is also twice the measure of minor arc QS. This is because minor arc PR is the sum of minor arcs QR and RP.
6. Now, we can relate the measures of these arcs to the angles they intercept.
Since angle QXS intercepts the arcs QS and XR, and minor arc QR is twice the measure of minor arc QS, we can conclude that the measure of angle QXS is half the measure of angle PXR.
7. We are given that the measure of angle PTR is 64 degrees.
Using this information, we know that angle PXR is also 64 degrees because angles PXR and PTR are subtended by the same arc (PR) on the circumference of the circle.
Finally, we can calculate the measure of angle QXS:
Since angle QXS is half the measure of angle PXR, which is 64 degrees, we can conclude that angle QXS is 64/2 = 32 degrees.
Therefore, the value of angle QXS is 32 degrees.