Question

GEOMETRY Please help me

Answer 1

Answer:

First option.

Step-by-step explanation:

In this case you need to remember that an angle formed by two intersecting chords is equal to the sum of the intercepted arcs divided by 2. This is:

$Angle\ formed\ by\ two\ intersecting\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)$

You can identify in the figure that the angle ∠1 is an angle formed by two intersecting chords. Therefore, since the intercepted arcs are SP and QR, you can say the following:

$m\angle 1=\frac{1}2}(mSP+mQR)$

You can observe that this matches with the first option.