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Byju's Answer

Standard VIII

Mathematics

Angle Sum Property of a Polygon

In the figure...

Question

In the figure given below, measure of $∠ A B C$ is

60^{0}

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70^{0}

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80^{0}

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50^{0}

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Solution

The correct option is C $60^{0}$
$∠ A B C + ∠ B A C = ∠ A C D$ (An exterior of a triangle is equal to the sum of the opposite interior angles)
$40^{\circ} + ∠ A B C = 100^{\circ}$
$∠ A B C = 100^{\circ} - 40^{\circ} = 60^{\circ}$
So option $A$ is correct

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Similar questions

Q. There are two shops that sell mobile phones of different price range and the data is given below. Mobile Price Range (

$

) Shop A Shop B

400 - 500

500 - 600

600 - 700

700 - 800

800 - 900

$123$	$342$
$232$	$374$
$122$	$394$
$166$	$329$
$187$	$322$

How many mobile phones are sold by both the shops in price range

$ 500 - $ 700

in total?

The following table gives the life times of 400 neon lamps :

(i)

Represent the given information with the help of histogram.

Life time (in hours)	Number of lamps
$300 - 400$	$14$
$400 - 500$	$56$
$500 - 600$	$60$
$600 - 700$	$86$
$700 - 800$	$74$
$800 - 900$	$62$
$900 - 1000$	$48$

(i i)

How many lamps have a life time more than

700

hours?

Q. The median of the following data in

525

. Find the missing frequency, if it is given that there are

100

observations in the data:

Class interval	Frequency	Class interval	Frequency
0-100	$2$	500-600	$20$
100-200	$5$	600-700	$f_{2}$
200-300	$f_{1}$	700-800	$9$
300-400	$12$	800-900	$7$
400-500	$17$	900-1000	$4$

Q. Find the mean of the following data .

Class Interval	Frequency
$0 - 100$	$2$
$100 - 200$	$5$
$200 - 300$	$4$
$300 - 400$	$12$
$400 - 500$	$17$
$500 - 600$	$20$
$600 - 700$	$20$
$700 - 800$	$9$
$800 - 900$	$7$
$900 - 1000$	$4$

The following table gives the lifetimes of 400 neon lamps:
$\begin{matrix} Lifetime (in hr) & 300 - 400 & 400 - 500 & 500 - 600 & 600 - 700 & 700 - 800 & 800 - 900 & 900 - 1000 Number of lamps & 14 & 56 & 60 & 86 & 74 & 62 & 48 \end{matrix}$
(i) Reperesent the given information with the help of a histogram.
(ii) How may lamps have a lifetime of more than 700 hours?

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In the figure given below, measure of ∠ABC is

The correct option is C 600∠ABC+∠BAC=∠ACD (An exterior of a triangle is equal to the sum of the opposite interior angles)40∘+∠ABC=100∘∠ABC=100∘−40∘=60∘So option A is correct

In the figure given below, measure of $∠ A B C$ is

The correct option is C $60^{0}$
$∠ A B C + ∠ B A C = ∠ A C D$ (An exterior of a triangle is equal to the sum of the opposite interior angles)
$40^{\circ} + ∠ A B C = 100^{\circ}$
$∠ A B C = 100^{\circ} - 40^{\circ} = 60^{\circ}$
So option $A$ is correct