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Olympiad Test: Triangle - 1 - Class 7 MCQ


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10 Questions MCQ Test Mathematics Olympiad Class 7 - Olympiad Test: Triangle - 1

Olympiad Test: Triangle - 1 for Class 7 2024 is part of Mathematics Olympiad Class 7 preparation. The Olympiad Test: Triangle - 1 questions and answers have been prepared according to the Class 7 exam syllabus.The Olympiad Test: Triangle - 1 MCQs are made for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Triangle - 1 below.
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Olympiad Test: Triangle - 1 - Question 1

Two angles of a triangle are equal and the third angle measures 70°. Find the measure of each of the unknown angles.

Detailed Solution for Olympiad Test: Triangle - 1 - Question 1

Let the measure of each unknown angle be x°. We know that the sum of the angles of a triangle is 180°. 
∴ x + x + 70 = 180° 
⇒ 2x = (180° – 70°)
⇒ 2x = 110°
⇒ x = 55°
Hence each unknown angle is 55°.

Olympiad Test: Triangle - 1 - Question 2

In a ∆XYZ, if ∠X = 90° and ∠Z = 48°, find ∠Y. 

Detailed Solution for Olympiad Test: Triangle - 1 - Question 2

We know that the sum of the angles of a triangle is 180°.

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Olympiad Test: Triangle - 1 - Question 3

Each of the two equal angles of an isosceles triangle is twice the third angle. Find the angles of the triangle.

Detailed Solution for Olympiad Test: Triangle - 1 - Question 3

Let the third angle be x°.
We know that the sum of the angles of a triangle is 180°. 
∴ 2x + 2x + x = 180° 
⇒ 5x = 180° 
⇒ x = 36°
So, the angles are (2 × 36)°, (2 × 36)° and (x)°
Hence, the angles of the triangles are 72°, 72°, 36°. 

Olympiad Test: Triangle - 1 - Question 4

Find the angles of a triangle which are in the ratio 4 : 3 : 2.

Detailed Solution for Olympiad Test: Triangle - 1 - Question 4

Let the measure of the given angles of the triangle be (4x)°, (3x)° and (2x)° respectively.
4x + 3x + 2x = 180°
⇒ 9x = 180°

So, the angles measure (4×20)°, (3 × 20)° and (2 × 20)° 
Hence, the angles of the triangle are 80°, 60°, 40°.

Olympiad Test: Triangle - 1 - Question 5

In the figure given alongside, x : y = 2 : 3 and ∠ACD = 130° find the values of x, y and z.

Detailed Solution for Olympiad Test: Triangle - 1 - Question 5

Let x = 2t, y = 3t, then 2t + 3t = 130° ⇒ t = 26°

∴ Sum of all angles of a triangle is 180°

Olympiad Test: Triangle - 1 - Question 6

A man goes 24m due east and then 10m due north. How far is he away from his initial position?

Detailed Solution for Olympiad Test: Triangle - 1 - Question 6

Let O be the initial position of the man. Let he cover OA = 24m due east and then AB = 10m due north.

Finally, he reaches the point B. Join OB.
OB2 = (OA2 + OB2) = {(24)2 + (10)2} m2
= (576 + 100) m2 = 676 m2

Hence, the man is at a distance at 26m from his initial position. 

Olympiad Test: Triangle - 1 - Question 7

The lengths of the sides of two triangles are given below. Which of them is right – angled?
(i) a = 8 cm, b = 5 cm, and c = 10 cm
(ii) a = 7 cm, b = 24 cm, and c = 25 cm

Detailed Solution for Olympiad Test: Triangle - 1 - Question 7

(i)
Here a  = 8 cm, b = 5cm  and c = 10c,
The largest side is c = 10cm.
a2 + b2 = {(8)2 + (5)2} cm2
= m (64 + 25) cm2 = 89 cm2 ≠ (10)2 cm2
a2 + b2 ≠ c2
∴ Given triangle is not right angled.
(ii) Here a = 7 cm, b = 24 cm and c = 25 cm
The largest side is c = 25 cm
a2 + b2 = {(7)2 + (24)2} cm2 = (49 + 576) cm2
= 625 cm2 = (25 cm)2 = c2
⇒ a2 + b2 = c2
Given triangle is right angled. 

Olympiad Test: Triangle - 1 - Question 8

Two poles of height 9 cm and 14m stand upright on a plane ground. If the distance between their feet is 12 m. Find the distance between their tops.

Detailed Solution for Olympiad Test: Triangle - 1 - Question 8

Let AB and CD be the given poles such that
AB = 9 m, CD = 14 m and AC = 12 m. Join BD.
From B, draw BL ⊥ CD.
DL = (CD – CL) = (CD – AB)
= (14 – 9) m = 5 m

BL = AC = 12 m
Now, in right ∆BLD, by Pythagoras theorem.
We have
BD2 = BL2 + DL2  = {(12)2 + (5)2}m2
= (144 + 25) m2 = 169 m2

Olympiad Test: Triangle - 1 - Question 9

In a ∆ABC it is given that ∠B = 37° and ∠C = 29°. Then ∠A = ?

Detailed Solution for Olympiad Test: Triangle - 1 - Question 9

We know that the sum of the angles of  a triangle is 180°.

Olympiad Test: Triangle - 1 - Question 10

In a ∆ABC, if  2∠A = 3, ∠B = 6∠C then ∠B = ?

Detailed Solution for Olympiad Test: Triangle - 1 - Question 10



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