Question

In a right angled triangle, if one acute angle is half the other, then the smallest angle is
O 150
O 30°
0 250
0 60°​

Answer 1

Answer:

let one acute angle is 2x°

then another acute angle is x°

so,2x+x+90=180

3x=180-90=90

x=90/3=30

the smallest angle is 30°

Answer 2

Answer:

The smallest angle is 30°

Step-by-step explanation:

Given,

In a right-angled triangle,  one acute angle is half the other

To find,

The smallest angle

Recall the concepts:

In a right-angled triangle, one angle measure 90°

The sum of three angles of a triangle = 180°

Solution:

Let x and y be the two acute angles of the right-angled triangle.

Then we have, the three angles of the triangle are x,y,90

Since one acute angle is twice the other we have,

y =  2x,

Hence the three angles of the triangle are x,2x and 90

Since the sum of three angles of a triangle = 180°, we have

x+2x+90 = 180

3x +90 = 180

3x = 90

x = 30

Hence the three angles of the triangle are 30°,60°,90°.

The smallest angle is 30°

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