Home » » In the diagram above, PQO is a diameter of the circle PQR. If < PSR = 145$$^{\circ}$$ find x$$^{\circ}$$...

# In the diagram above, PQO is a diameter of the circle PQR. If < PSR = 145$$^{\circ}$$ find x$$^{\circ}$$...

### Question

In the diagram above, PQO is a diameter of the circle PQR. If < PSR = 145$$^{\circ}$$ find x$$^{\circ}$$

### Options

A) 35$$^{\circ}$$

B) 55$$^{\circ}$$

C) 25$$^{\circ}$$

D) 45$$^{\circ}$$

### Explanation:

Construction RQ

< PRQ = 90$$^{\circ}$$(amgle substended at the circumfernce of a circle by diameter). Also in figure PQRS

< PQS + PSQ = 180(supplementary angle)

< PQS = 180 - 145 = 35

In $$\bigtriangleup$$PRQ x = 180 - 935 = 90)

x = 55

## Dicussion (1)

• Construction RQ

< PRQ = 90$$^{\circ}$$(amgle substended at the circumfernce of a circle by diameter). Also in figure PQRS

< PQS + PSQ = 180(supplementary angle)

< PQS = 180 - 145 = 35

In $$\bigtriangleup$$PRQ x = 180 - 935 = 90)

x = 55