Question

Two acute angles are in the ratio 1:5. Find the 3 angles of the triangle

Answer 1

Given :-

• Two acute angles are in ratio 1 : 5

Solution :-

As we know that,

The sum of angles of triangles are 180°

Here, Two sides are in ratio 1 : 5

Let's ratios of acute angles be 1x and 5x

As we know that the acute angles are less than 90°

Now, Implies this

180° - 90° = x + 5x

90° = 6x

x = 90/6 = 15°

Thus, The value of x = 15°

The value of first angle = x = 15°

The value of second angle = 5 * 15 = 75°

The value of third angle be a

Now, Using Angle sum property

15° + 75° + a = 180°

a + 90° = 180°

a = 180° - 90°

a = 90°

Hence, The value of third angle is 90° $.$

Answer 2

Answer:

Given :-

Two acute angles are in ratio 1 : 5

To Find :-

3 angles

Solution :-

As we know that Acute angle is 90⁰. Assuming ratio as x and 5x

90 = x + 5x

90 = 6x

90/6 = x

15 = x

2 angles are :- 15 and 5(15) = 75

Now,

By using angles sum property

15 + 75 + a = 180

90 + a = 180

a = 180 - 90

a = 90

Angles are

$\sf \: 15 \: \: \: 75 \: \: and \: \: 90$