Question

the angle of the triangle are in the ratio 5:3:7 , the triangle is

A. an acute angled triangle
B. an obtuse angled triangle
C. a right triangle
D. an isosceles triangle

(please answer correctly)

THANKS...​

Answer 1

Step-by-step explanation:

The angles of a triangle are in the ratio 5:3:7

Let these three angles be 5x°,3x°,7x°

By condition,

5x°+3x°+7x° = 180°

5x+3x+7x = 180

15x = 180

x = 180/15

x = 12

The angles are

(5×12)°=60°

(3×12)° =36°

(7×12)° =84°

After observing the angles we conclude that the triangle is A. an acute angled triangle

Answer 2

Given : The angles of a triangle are in the ratio 3:5:7.  

To Find : Triangle is:

(a) Acute angled

(b) obtuse angled

(c) Right angled

(d) an isosceles triangle

​

Solution:

The angles of a triangle are in the ratio 3:5:7.  

Let say angles are 3x , 5x  and 7x

Using triangle angle sum theorem that sum of all the angles of a triangle is 180°

3x + 5x + 7x = 180°

=> 15x = 180°

=> x = 12°

angles are 3x , 5x  and 7x

3(12°) = 36°

5(12°) = 60°

7(12°) = 84°

Hence triangle is Acute angled  triangle

Acute angle whose measure is between 0° and 90°

Right angle whose measure is 90°

Obtuse angle  whose measure is between 90° and 180°

Triangle is Acute angled triangle if all 3 angles are acute

Triangle is Right angled triangle if one angle is right angle

Triangle is Obtuse angled triangle if one angle is obtuse angle

An isosceles triangle  is triangle having 2 equal sides

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