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Chord Properties of Circles

In the circle...

Question

In the circle shown below, $J K = 2$ and $L M = 2$ . What is the value of $x$ ?

55^{o}

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45^{o}

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75^{o}

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65^{o}

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Solution

The correct option is C $75^{o}$
According to the theorem:
In a circle, or congruent circles, congruent chords have congruent arcs.
So, $¯ ¯¯¯¯¯¯ ¯ J K ≅ ¯ ¯¯¯¯¯¯¯¯ ¯ L M$
$ˆ J K ≅ ˆ L M$
$ˆ L M = 75^{o}$
Therefore, $x = 75^{o}$

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Similar questions

{sin}^{2} 65^{o} + {sin}^{2} 25^{o} + {cos}^{2} 35^{o} + {cos}^{2} 55^{o}

O

S P

∠ S R T = 65^{o}

x

y

z

△ A B C

∠ A = 75^{o}, ∠ B = 65^{o}

∠ C

B A ∥ D F, A D ∥ F G, ∠ B A C = 65^{o}

∠ A C B = 55^{o}

∠ F G H

α = 75^{o}

β = 55^{o}

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