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# In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Ca...

### Question

In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Calculate < PST.

A) 54o

B) 44o

C) 34o

D) 27o

### Explanation:

In the diagram above, x1 = 180o - 117o = 63o(opposite angles of a cyclic quad.)

x1 = x2 (base angles of isos. $$\Delta$$)

x1 + x2 + $$\alpha$$ = 180o (sum of angles of a $$\Delta$$

63o + 63o + $$\alpha$$ = 180o

$$\alpha$$ = 180o - (63 + 63)o

= 54o

## Dicussion (1)

• In the diagram above, x1 = 180o - 117o = 63o(opposite angles of a cyclic quad.)

x1 = x2 (base angles of isos. $$\Delta$$)

x1 + x2 + $$\alpha$$ = 180o (sum of angles of a $$\Delta$$

63o + 63o + $$\alpha$$ = 180o

$$\alpha$$ = 180o - (63 + 63)o

= 54o