In this figure, lines a and b are parallel lines. And we are given the measure of angles 10, 7, and 16 which are shown in the following diagram:
Since we are asked for angle 6, we represent it with an x.
To solve this problem, first, we use the properties of parallel lines. In specific we look for vertical angles in line d. Vertical angles are angles opposite to the same vertex, and they are equal.
The vertical angle of m<16 is m<18, thus m<18=139:
Now, m<18 has a corresponding angle (this is also according to the properties of the vertical lines a and b), the corresponding angle to m<18 is shown in yellow:
Since corresponding angles are equal, the yellow angle is equal to 139. But as you can see, the yellow angle is the sum of 47° and x:
From this equation, we can solve to find the value of x (which is the measure of angle 9).
We solve for x by subtracting 47 to both sides of the equation:
Since x=92, angle 6 is equal to 92.
Answer:
m<6=92°