Question

the angles of triangle PQR are in the ratio of 1:5:6 find angle P,Q,R​

Answer 1

Answer:

1:5:6

let the angles be 1x,5x,6x

1x+5x+6x=180

12x=180

x=180÷12

x=15

therefore,angles are:

1x =15

5x=5×15=75

6x=6×15=90

Answer 2

Diagram:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf P }\put(0.5,-0.3){ \bf Q }\put(5.2,-0.3){ \bf R }\end{picture}$

Given:

• Angles of Triangle are in the ratio 1:5:6

To find

⟶ ∠P, ∠Q, ∠R

Method:

Let the angles be 1x, 5x and 6x

First let's understand the concept.

Concept Used:

Sum of all angles in a Triangle is always 180°

1x + 5x + 6x = 180°

⇒ 12x = 180°

⇒ x = 180° ÷ 12

⇒ x = 15°

Now let's find out the angles.

∠P = 1x = 15°

∠Q = 5x = 5(15) = 75°

∠R = 6x = 6(15) = 90°

∴ The angles of Triangle are 15°, 75°, 90°

Verification:

You can verify the angle measures by adding the angles.

Here,

15° + 75° + 90° = 180°

180° = 180°

LHS = RHS

Hence Verified.