An obtuse angle is formed by two adjacent angles with majors X -5 and 3X if the resulting angle major is 107, what is the angle measure of each of the unknown two angles round to the nearest whole number?

Question

20 and 87
28 and 70
32 and 75
23 and 84

Answer 1

To find the measure of each unknown angle, we can set up an equation.

Let's assume the measure of the smaller adjacent angle is X.

Since the resulting angle major is 107, we can set up the equation:

X - 5 + 3X = 107

Combining like terms:

4X - 5 = 107

Adding 5 to both sides:

4X = 112

Dividing both sides by 4:

X = 28

Therefore, the measure of the smaller adjacent angle is 28 degrees.

To find the measure of the larger adjacent angle, we can substitute X back into the equation:

3X = 3(28) = 84

Therefore, the measure of the larger adjacent angle is 84 degrees.

Rounding these angles to the nearest whole number, we get:

28 and 84

So, the correct answer is 23 and 84 (since the first angle major is -5 + X, it is negative when X = 23).