Question

if the angle between two radii of a circle is 130°, the angle between the tangents at the ends of radii is..... ​

Answer 1

Answer:

50°

Step-by-step explanation:

ABCD is quadrangle ⇒ m∠A + m∠B + m∠C + m∠D = 360°

AB ⊥ AD and CD ⊥ CB (property of tangent to the circle)

90° + x° + 90° + 130° = 360° ⇒ x = 360° - 310° = 50°

m∠B = 50°

Answer 2

Given :- If the measure of angle between two radii of a circle is 130°, then the measure of angle between tangents at the outer end of radii is …………?

Solution :-

given that,

→ ∠AOB = 130° .

→ OA = OB = radius .

we know that,

• Radius is perpendicular to the tangent at the point of contact .
• sum of interior angles of a quadrilateral is 360° .

So,

→ ∠OAC = ∠OBC = 90° .

therefore,

→ ∠AOB + ∠OAC + ∠OBC + ∠ACB = 360° .

→ 130° + 90° + 90° + ∠ACB = 360°

→ 310° + ∠ACB = 360°

→ ∠ACB = 360° - 310°

→ ∠ACB = 50° (Ans.)

Hence, the measure of angle between tangents at the outer end of radii is 50° .

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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