Is the measure of angles of a triangle are in the ratio of 3 ratio 4 ratio 5 What is the measure of the smallest angle of the triangle?

Text Solution

Solution : Given: The angles of a triangle are in the ratio `3:4:5`.<br>Let the measure of the angles be `3x`, `4x`, `5x`<br>By the sum of the angles of a triangle`=180^@`<br>`3x+4x+5x=180`<br>`=>12x=180^@`<br>`=>x=180^@/12`<br>`=>x=15^@`<br>`therefore` Smallest angle`=3x`<br>`=3×15^@`<br>`=45^@`<br>Hence, the measure of the smallest angle of the triangle`=45^@`.

In the given figure, measures of the angles of ΔABC are in the ratio 3 : 4 : 5. We need to find the measure of the smallest angle of the triangle.

Let us take,

∠A = 3x

∠B = 4x

∠C = 5x

Now, applying angle sum property of the triangle in ΔABC, we get,

∠A + ∠B + ∠C = 180°

   3x + 4x + 5x = 180°

                12X = 180°

                   `x = (180°)/ 12`

                     x = 15°

Substituting the value of x in ,∠A,∠Band∠C

∠A = 3(15°) = 45

∠B = 4(15V) = 60

∠C = 5(15°) = 75°

Since, the measure of ∠A is the smallest

Thus, the measure of the smallest angle of the triangle is 45°