Question

Consider ΔABC with incenter D. If m∠ACB = 3x + 54 and m∠ACD = x + 31, what is m∠ACD in degrees?

Answer 1

To find the measure of angle ACD, set up an equation using the given angles and solve for x. Then, substitute the value of x back into the equation to find the measure of angle ACD.

Step-by-step explanation:

To find the measure of angle ACD, we need to use the fact that the incenter of a triangle is equidistant from the three sides of the triangle. This means that AD = CD. We can set up an equation using the given angles as follows:

m∠ACD = m∠ACB - m∠ACD

x + 31 = 3x + 54 - x

31 = 2x + 54

2x = -23

x = -11.5

So, m∠ACD = -11.5 + 31 = 19.5°