Question

in figure Rs is a tangent to the circle at a l and m n is a diameter if angle NMLis equal to 30 degree determine angle rlm

Answer 1

We recall the concept of circle

The circle is a round-shaped object

Given:

Angle NML$=30^{0}$

Since MN and RS are parallel.

Angle NML= Angle RLM....................[Alternate angles]

Angle RLM$=30^{0}$

Answer 2

Answer:

The value of ∠RLM is 30°.

Step-by-step explanation:

Given:-

R is the tangent

O is the center of the circle

∠NML is 30°

To find:-

∠RLM=?

Construction:-

Join LN

Solution:-

∠LMN = ∠LNO = 30°

In ΔMLN

30° + 30° +∠MLN = 180° (∵ Angle sum property)

60° + ∠MLN + 180°

∠MLN = 180° - 60°

∠MLN = 120°

Since O is the center of the circle, OL is the radii of the circle

∴∠OLM = 1/2 ∠MLN

∠OLM = 60°

Now, ∠OLM + ∠RLM = ∠OLR

∠OLM + ∠RLM = 90 (∵ Tangent at any point of contact subtend 90°)

60° +  ∠RLM = 90°

∠RLM = 90° - 60°

∠RLM = 30°

Hence, ∠RLM = 30°

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