The angles of a triangle are in the ratio 3:5:7. The triangle is
(a) Acute angled
(b) obtuse angled
(c) Right angled
(d) an isosceles triangle
Answers
Step-by-step explanation:
Let the angles of the triangle be 3x, 5x and 7x
Now, as we knew the sum of all the three interior angles of a triangle is 180°.
According to the question:-
→ 3x + 5x + 7x = 180°
→ 15x = 180°
→ x = 180°/15
→ x = 12°
Therefore, all the three angles of the triangle are as follows:-
Therefore, all the three angles of the triangle are as follows:-
• 1st Angle → 3x = 3×12° = 36°
• 2nd Angle → 5x = 5×12° = 60°
• 3rd Angle → 7x = 7×12° = 84°
Since, the measure of all the three Angles of the given triangle is less than 90° i.e 36°, 60° and 84°, the given triangle is an Acute Angled Triangle.
Please mark as “Brainliest Answer”...
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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