Question

One angle of a triangle measures 30°. If the measures of the other two angles are in the ratio 3:7, the measure of the largest angle of the triangle is

Answer 1

To find the measure of the largest angle in the triangle, let's denote the measures of the other two angles as 3x and 7x, where x is a common factor. The sum of all angles in a triangle is 180°.

Given that one angle measures 30°, we have:

30° + 3x + 7x = 180°

Combining like terms:

30° + 10x = 180°

Subtracting 30° from both sides:

10x = 150°

Dividing both sides by 10:

x = 15°

Now we can find the measures of the other two angles:

3x = 3 * 15° = 45°

7x = 7 * 15° = 105°

Therefore, the measure of the largest angle in the triangle is 105°.

Answer 2

B)105

Explanation:

Let's denote the measures of the other two angles as 3x and 7x, where x is a constant. We know that the sum of the angles in a triangle is 180 degrees.

So, we can set up an equation to find x:

30 + 3x + 7x = 180

Combining like terms:

30 + 10x = 180

Subtracting 30 from both sides:

10x = 150

Dividing both sides by 10:

x = 15

Now we can find the measures of the other two angles:

3x = 3 * 15 = 45

7x = 7 * 15 = 105

The largest angle of the triangle is 105 degrees.