Question

In a rhombus ABCD with diagonals AC and BD intersecting at X, if angle AXC = 60 degrees and angle BXC = 80 degrees, what is the measure of angle AXB?

1) 40 degrees
2) 50 degrees
3) 60 degrees
4) 70 degrees

Answer 1

The measure of angle AXB in the rhombus is 40 degrees, determined by using the properties of the diagonals in a rhombus and the complementary angles at vertex X.

Step-by-step explanation:

The student is asking for the measure of angle AXB in a rhombus with given angles at vertex X. To solve this, we will use the property that the diagonals of a rhombus bisect each other at right angles. Therefore, triangle AXC and triangle BXC are right triangles, and the angles at X must add up to 90 degrees because they are complementary. Given that angle AXC is 60 degrees and angle BXC is 80 degrees, we can deduce that angle AXD (which is complimentary to angle AXC) is 30 degrees, and angle BXD (complementary to angle BXC) is 10 degrees. Now, to find angle AXB, we add these two angles together: 30 degrees + 10 degrees = 40 degrees.