The measures of the angles of a triangle are in the extended ratio 3 : 5 : 7. What is the measure of the smallest angle?
a. 12°
b. 36°
c. 60°
d. 84°
The sum of the angles in a triangle is always 180 degrees. Let x be the common factor that multiplies the ratios 3, 5, and 7. Then, the angles can be expressed as 3x, 5x, and 7x.
The sum of these angles is:
3x + 5x + 7x = 15x
Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:
15x = 180
Solving for x, we get:
x = 12
Therefore, the angles are:
3x = 36 degrees
5x = 60 degrees
7x = 84 degrees
The smallest angle is 36 degrees, so the answer is (b) 36°.
To find the measure of the smallest angle in a triangle, we need to find the ratio of the angles.
Let's assume the measures of the angles are 3x, 5x, and 7x respectively.
To find x, we add up the measures of the angles in a triangle, which sum up to 180 degrees:
3x + 5x + 7x = 180 degrees
Simplifying, we have:
15x = 180 degrees
Dividing both sides by 15, we get:
x = 12 degrees
Now, we can find the measure of the smallest angle by plugging in the value of x:
3x = 3 * 12 degrees = 36 degrees
Therefore, the measure of the smallest angle is 36 degrees.
So, the correct answer is b. 36°.