Question

Find the value of x in this figure?

47


53


43


57

Answer 1

Assuming PQ is tangent to the circle, ∠OQP = 90°

90 + 43 + x = 180° (Sum of all angles in a triangle is 180)

x = 180 - 90 - 43 = 47°

Answer: x = 47°

Answer 2

Option A.

Explanation:

We know that radius of a circle is perpendicular to its tangent at the point of tangency.

`\angle OQP=90^(\circ)`

According to the angle sum property, the sum of interior angles of a triangle is 180 degrees.

Using angle sum property we get

`x^(\circ)+90^(\circ)+43^(\circ)=180^(\circ)`

`x^(\circ)+133^(\circ)=180^(\circ)`

`x^(\circ)=180^(\circ)-133^(\circ)`

`x^(\circ)=47^(\circ)`

`x=47`

The value of x is 47.

Hence, the correct option is A.