If abd = 74º what are abc and dbc?

Step-by-step explanation:

5x-3+5x+7=10x+4

10x+4=74

10x=74-4

10x=70

x=70/10=7

for abc

5x-3

5(7)-3

35-3=32

for dbc

5x+7

5(7)+7

35+7=42

∠ABC = 32

∠DBC = 42

Step-by-step explanation:

∠ABD = ∠ABC + ∠DBC

74 = 5x - 3 + 5x + 7

= 5x + 5x + 7 - 3

74 = 10x + 4

74 - 4 = 10x

70 = 10x

x = 70 / 10

x = 7

∠ABC = 5x - 3

= 5 ( 7 ) - 3

= 35 - 3

∠ABC = 32

∠ABD = ∠ABC + ∠DBC

∠DBC = ∠ABD - ∠ABC

= 74 - 32

∠DBC = 42

In place of t, or theta, I'm going to utilize x instead. So the equation is -3*cos(x) = 1. Get everything to one side and we have -3*cos(x)-1 = 0

Let f(x) = -3*cos(x)-1. The goal is to find the root of f(x) in the interval [0, 2pi]

I'm using the program GeoGebra to get the task done of finding the roots. In this case, there are 2 roots and they are marked by the points A and B in the attachment shown

A = (1.91, 0)
B = (4.37, 0)

So the two solutions for theta are
theta = 1.91 radians
theta = 4.37 radians