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# In the diagram, O is the centre, $$\bar{RT}$$ is a diameter, < PQT = 33$$^o$$...

### Question

In the diagram, O is the centre, $$\bar{RT}$$ is a diameter, < PQT = 33$$^o$$ and <TOS = 76$$^o$$. Using the diagram, calculate the value of angle PTR.

### Options

A) 73o

B) 67o

C) 57o

D) 37o

The correct answer is C.

### Explanation:

In the diagram given, < PRT = 3$$^o$$ (Change in same segment)

< TPR = 90$$^o$$ (angle in a semicircle)

Hence, < PTR = 180$$^o$$ - (90 + 33)$$^o$$

= 180$$^o$$ - 123$$^o$$

= 57$$^o$$

## Dicussion (1)

• In the diagram given, < PRT = 3$$^o$$ (Change in same segment)

< TPR = 90$$^o$$ (angle in a semicircle)

Hence, < PTR = 180$$^o$$ - (90 + 33)$$^o$$

= 180$$^o$$ - 123$$^o$$

= 57$$^o$$

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