1. If m∠BAC = 38° and m∠DEC = 100°, then what is the value of x? Explain and show all work.
explain the diagram. include all labels.
To find the value of x, we need to use the fact that the sum of the angles in a triangle is always equal to 180 degrees.
First, let's identify the angles we know:
- m∠BAC = 38°
- m∠DEC = 100°
Since the angles BAC and DEC are vertically opposite angles (formed by intersecting lines), they are equal:
m∠BAC = m∠DEC = 38°
Now, we can set up an equation to find the value of x:
38° + x + 100° = 180°
Simplifying the equation:
138° + x = 180°
Next, let's isolate x by subtracting 138° from both sides of the equation:
x = 180° - 138°
Calculating the value of x:
x = 42°
Therefore, the value of x is 42°.
In summary, to find the value of x, we used the fact that the sum of the angles in a triangle is 180°. We set up an equation by equating the angle measures and then solved for x by simplifying the equation and isolating the variable.