MATH SOLVE

5 months ago

Q:
# PLEASE ANSWER ASAP 30 POINTS IF CORRECT!!! AND MARKED BRAINIESTDrag the tiles to the boxes to form correct pairs. Not all tiles will be used.With reference to the figure, match the angles and arcs to their measures.ONLY 4 POSSIBLE MATCHES!1.DFA2.ARC CE3.EOB4.COB5.OCAA.124 deg.B.144 deg.C.58 deg.D.122 deg

Accepted Solution

A:

1. DFA = 58 deg.
Look at triangle DFA. You'll easily determine the other 2 angles to be 56 and 66 degrees because they're supplementary angles to 124 and 114. So the 3rd angle has to be 180 - 56 - 66 = 58 degrees.
2. Arc CE = 124 deg.
Look at quadrilateral DEOC. Angle CDE is 56 degrees because it's a supplementary angle to 124. Angles OCD and OED are both 90 because the circle is tangent to the lines. Leaving 360-90-90-56 = 125 degrees for the arc.
3. EOB = 122 deg.
Look at quadrilateral EFBO. We already know that angle EFB is 58 degrees due to problem 1. The other 2 angles are 90 degrees for the same reason as in problem 2. So the remaining angle is 360 - 58 - 90 - 90 = 122.
4. COB = 114 deg.
One of the angles is the supplementary angle to 114, so 180-114 - 66. The other 2 angles are 90. So the last angle is 360 - 90 - 90 - 66 = 114.
5. OCA = 90 deg
Line segment AD is tangent to the circle at point C. So the radius OC is perpendicular to the line segment AD at point C. So angle OCA is 90 degrees.