Given that <APD=4x+123,<DPC=-5x-3 and <CPB=6x+105,find the measure of <DPC.
If this is a triangle then they sum to 180 degrees
4x+ 123 -5x-3 + 6x + 105 = 180
5x + 225 = 180
find x and then substitute the value into -5x -3 to find <DPC
Thanks John!
How could it be a triangle with P in the middle of all three angles?
I think we are missing information.
There is no info missing
Try to draw a triangle with angles
APD
DPC
CPB
To find the measure of ∠DPC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
In this case, we have ∠APD + ∠DPC + ∠CPB = 180°.
We are given that ∠APD = 4x + 123°, ∠DPC = -5x - 3°, and ∠CPB = 6x + 105°.
Substituting these values into the equation, we get:
(4x + 123) + (-5x - 3) + (6x + 105) = 180°.
Simplifying this equation, we have:
4x - 5x + 6x + 123 - 3 + 105 = 180°.
Combining like terms, we get:
5x + 225 = 180°.
Now, we can solve for x:
5x = 180° - 225.
5x = -45°.
Dividing both sides by 5, we have:
x = -9°.
Now that we have found the value of x, we can substitute it back into the equation for ∠DPC:
∠DPC = -5x - 3°.
∠DPC = -5(-9) - 3°.
∠DPC = 45° - 3°.
∠DPC = 42°.
Therefore, the measure of ∠DPC is 42 degrees.