Solve for z. I got z=72 degrees and i don't know how I got it. The circle has diameter AB then another diameter CD. Arc AD = 40 degrees then angle DEB = 124 degrees and z = BC. The diameter DC intersects diameter AB. Please help i can't figure it out and it's now almost 2am.
I must be missing something here.
If AB and CD are diameters, then AD = BC, since the diameters must intersect in the center of the circle.
No idea where E is.
To solve for z, we need to analyze the given information and use some properties of circles and angles.
1. Start by drawing a diagram to represent the given information. Draw the circle with diameter AB and another diameter CD intersecting at point E. Label the arc AD as 40 degrees and the angle DEB as 124 degrees. Label z as BC.
2. Recall that the measure of an arc is twice the measure of its corresponding central angle. Since arc AD is 40 degrees, its corresponding central angle (angle AED) will be half that, which is 20 degrees.
3. Notice that angles AED and CEB are vertical angles (opposite angles formed by intersecting lines), and they are congruent. Therefore, angle CEB is also 20 degrees.
4. Since the sum of angles in a triangle is 180 degrees, we can find angle BCE. From step 3, we know angle CEB is 20 degrees. The measure of angle B is 180 degrees minus the sum of angle CEB and angle DEB. So, angle B is 180 - (20 + 124) = 36 degrees.
5. Finally, since angles BCE and B are vertical angles, they are congruent. Therefore, z (BC) also measures 36 degrees.
So, z = 36 degrees.
In summary, to solve for z, we used the properties of circles (arc and central angles), vertical angles, and the sum of angles in a triangle to find that z is equal to 36 degrees.