Question

angles of triangles are in the ratio 3:4:5 find the measure of each angle

Answer 1

Note: the sum of all angles of triangle is 180 °
so,
3x+4x+5x= 180
12x=180
x=180/12= 15

so first angle is = 3×15=45°
second angl= 4×15=60°
third angle= 5×15=75°


45+60+75=180
180=180

Answer 2

Angles of triangle are 45°,60°, and 75°.

Given:

• Angles of triangle are in the ratio 3:4:5.

To find:

• Find the measure of each angle.

Solution:

Concept to be used:

Sum of internal angles of triangle= 180°.

Step 1:

Let the common ratio of angles be 'k'.

So,

$3k + 4k + 5k = 180$

$12k = 180$

$k = \frac{180}{12}$

$\bf k = 15$

The common ratio of angles is 15.

Step 2:

Find the angles.

As, ratio of angles are 3:4:5 and the common ratio is 15,so

Angles are

$= 3 \times 15 \\ \bf = {45}^{ \circ} \: \: \: \: \:$

$= 4 \times 15 \\ \bf = {60}^{ \circ} \: \: \: \: \: \:$

$= 5\times 15 \\ \bf = {75}^{ \circ} \: \: \: \: \: \:$

Thus,

Angles of triangle are 45°,60°, and 75°.

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