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# In the diagram, $$\bar{PF}$$, $$\bar{QT}$$, $$\bar{RG}$$ intersect at S and PG||...

### Question

In the diagram, $$\bar{PF}$$, $$\bar{QT}$$, $$\bar{RG}$$ intersect at S and PG||RG. If < SPQ = 113o and < RST = 220o, find < PSQ.

A) 22o

B) 45o

C) 67o

D) 89o

### Explanation:

In In the diagram given, $$\alpha$$ = 22$$^{\circ}$$ (vertically opp. angles), $$\alpha$$ = $$\beta$$ (alternate angles)
< PSQ + 133$$^{\circ}$$ + $$\beta$$ = 180$$^{\circ}$$ (sum of angles of a $$\Delta$$)
< PSQ + 133$$^{\circ}$$ + 22$$^{\circ}$$ = 180$$^{\circ}$$
< PSQ = 180$$^{\circ}$$ - (133 + 22)$$^{\circ}$$
45$$^{\circ}$$

## Dicussion (1)

• In In the diagram given, $$\alpha$$ = 22$$^{\circ}$$ (vertically opp. angles), $$\alpha$$ = $$\beta$$ (alternate angles)
< PSQ + 133$$^{\circ}$$ + $$\beta$$ = 180$$^{\circ}$$ (sum of angles of a $$\Delta$$)
< PSQ + 133$$^{\circ}$$ + 22$$^{\circ}$$ = 180$$^{\circ}$$
< PSQ = 180$$^{\circ}$$ - (133 + 22)$$^{\circ}$$
45$$^{\circ}$$