In each of the following- the measures of three angles are given- State in which cases- the angles can possibly be those of a triangle-i- 63 deg- 37 deg- 80 deg-ii- 45 deg- 61 deg- 73 deg-iii- 59 deg- 72 deg- 61 deg-iv- 45 deg- 45 deg- 90 deg-v- 30 deg- 20 deg- 125 deg-

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Standard VII

Mathematics

Types of Triangles Based on Angles

In each of th...

Question

In each of the following, the measures of three angles are given. State in which cases, the angles can possibly be those of a triangle:
(i) 63°, 37°, 80°
(ii) 45°, 61°, 73°
(iii) 59°, 72°, 61°
(iv) 45°, 45°, 90°
(v) 30°, 20°, 125°

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Solution

$(i) We know that the sum of all the three angles of a triangle is equal to 180 ° . Now, let us find the sum of 63 °, 37 ° and 80 ° . 63 ° + 37 ° + 80 ° = 180 ° The sum of 63 °, 37 ° and 80 ° is equal to 180 ° . Hence, we can say that the given angles can be those of a triangle .$
$(ii) We know that the sum of all the three angles of a triangle is equal to 180 ° . Now, let us find the sum of 45 °, 61 ° and 73 ° . 45 ° + 61 ° + 73 ° = 179 ° The sum of 45 °, 61 ° and 73 ° is not equal to 180 ° . Hence, we can say that the given angles cannot be those of a triangle .$
$(iii) We know that the sum of all the three angles of a triangle is equal to 180 ° . Now, let us find the sum of 59 °, 72 ° and 61 ° . 59 ° + 72 ° + 61 ° = 192 ° The sum of 59 °, 72 ° and 61 ° is not equal to 180 ° . Hence, we can say that the given angles cannot be those of a triangle .$
$(iv) We know that the sum of all the three angles of a triangle is equal to 180 ° . Now, let us find the sum of 45 °, 45 ° and 90 ° . 45 ° + 45 ° + 90 ° = 180 ° The sum of 45 °, 45 ° and 90 ° is equal to 180 ° . Hence, we can say that the given angles can be those of a triangle .$
$(v) We know the sum of all the three angles of a traingle is equal to 180 ° . Now, let us find the sum of 30 °, 20 ° and 125 ° . 30 ° + 20 ° + 125 ° = 175 ° The sum of 30 °, 20 ° and 125 ° is not equal to 180 ° . Hence, we can say that the given angles cannot be those of a triangle .$
Therefore, we can conclude that in (i) and (iv), the angles can be those of a triangle.

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Similar questions

Q. In each of the following, the measures of three angles are given. State in which cases, the angles can possibly be those of a triangle:
(i) 63°, 37°, 80°
(ii) 45°, 61°, 73°
(iii) 59°, 72°, 61°
(iv) 45°, 45°, 90°
(v) 30°, 20°, 125°

The measures of some angles are given below. Write the measures of their complementary angles.

(i)

40^{\circ}

(ii)

63^{\circ}

(iii)

45^{\circ}

(iv)

55^{\circ}

(v)

20^{\circ}

(vi)

90^{\circ}

(vii)

x^{\circ}

Question 6

In a triangle, one angle is of $90^{\circ}$ . Then,

i) The other two angles are $45^{\circ}$ each.
ii) In remaining two angles, one angle is $90^{\circ}$ and other is $45^{\circ}$
iii) Remaining two angles are complementary

In the given option(s) which is true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Q. Diagonals of a quadrilateral ABCD bisect each other. If ∠A= 45°, then ∠B =

(i) 115°

(ii) 120°

(iii) 125°

(iv) 135°

Q. Each angle of an equilateral triangle measures
(a) 30°
(b) 45°
(c) 60°
(d) 80°

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In each of the following, the measures of three angles are given. State in which cases, the angles can possibly be those of a triangle: (i) 63°, 37°, 80° (ii) 45°, 61°, 73° (iii) 59°, 72°, 61° (iv) 45°, 45°, 90° (v) 30°, 20°, 125°

In each of the following, the measures of three angles are given. State in which cases, the angles can possibly be those of a triangle:
(i) 63°, 37°, 80°
(ii) 45°, 61°, 73°
(iii) 59°, 72°, 61°
(iv) 45°, 45°, 90°
(v) 30°, 20°, 125°