PQ and PR are two tangent to circle with centre O , if angle QPR is 4x-1 , Angle QOR is 3x-8 , find x
Answers
The value of 'x' is 27°
Given:
PQ and PR are two tangents to circle with center O,
The measure of ∠ QPR = 4x-1, ∠QOR = 3x-8
To find:
Find the value of x
Solution:
Given that PQ and PR are two tangents to circle with center O.
Draw the radius from the center to the tangents as shown figure
Here the radius drawn to the tangent will perpendicular to the tangent
=> ∠PQO = ∠PRO = 90°
From figure PQOR is quadrilateral
As we know the sum of the interior angles of a quadrilateral = 360°
=> ∠QPR + ∠QOR + ∠PQO + ∠PRO = 360°
=> 4x-1 + 3x-8 + 90° + 90° = 360°
=> 7x - 9 = 360° - 180°
=> 7x = 180°+ 9°
=> 7x = 189
=> x = 27°
Therefore,
The value of 'x' is 27°
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The value of 'x', the common measure of the angles QPR and QOR, is 27°.
The value of 'x' in this problem can be found by using the information given about two tangents PQ and PR drawn to a circle with center O. By drawing the radius from the center to the tangents, we can see that the angles PQO and PRO are 90 degrees each. Additionally, the sum of the interior angles of the quadrilateral PQOR is 360 degrees.
By using these observations and substituting the known values, we can arrive at the equation
7x - 9 = 360 - 180.
Simplifying this equation, we have
7x = 189,
which can be further divided by 7 to get
x = 27 °.
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