Find the value of - in the given figure-

The correct option is A 50^∘∠ ABC = 40^∘ [Given] ∠ ACB = 90^∘ [Angle in semicircle] In ABC, ∠ CAB + ∠ ACB + ∠ ABC = 180^∘ [Angle sum property] ∠ CAB + 90^∘ + ...

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Standard IX

Mathematics

Theorem on Cyclic Quadrilateral and Its Converse

Find the valu...

Question

Find the value of 𝑥 in the given figure.

50^{\circ}

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55^{\circ}

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60^{\circ}

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65^{\circ}

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Solution

The correct option is A $50^{\circ}$
$∠ A B C = 40^{\circ}$ [Given]
$∠ A C B = 90^{\circ}$ [Angle in semicircle]

In $△ A B C$ ,
$∠ C A B + ∠ A C B + ∠ A B C = 180^{\circ}$
[Angle sum property]

$∠ C A B + 90^{\circ} + 40^{\circ} = 180^{\circ}$
$∠ C A B = 180^{\circ} - 90^{\circ} - 40^{\circ}$
$∠ C A B = 50^{\circ}$

Now, $∠ C D B = ∠ C A B$
[ Angle is on same segment]

This implies $x = 50^{\circ}$

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Q. Estimate the median for the following data given below

:

Marks	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$
Students	$50$	$40$	$30$	$20$	$10$

Q. Find the median :

Weight	No of students
$40 - 45$	$2$
$45 - 50$	$3$
$50 - 55$	$8$
$55 - 60$	$6$
$60 - 65$	$6$
$65 - 70$	$3$
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Find the value of 𝑥 in the given figure.

The correct option is A 50∘∠ABC=40∘ [Given] ∠ACB=90∘ [Angle in semicircle] In △ABC, ∠CAB+∠ACB+∠ABC=180∘ [Angle sum property] ∠CAB+90∘+40∘=180∘ ∠CAB=180∘−90∘−40∘ ∠CAB=50∘ Now, ∠CDB=∠CAB [ Angle is on same segment] This implies x=50∘