The measure of angle FQD in the figure is 95 degrees.
1. Identify relevant triangles:
First, notice that triangles DFQ and DPQ share side DQ.
2. Apply angle relationship:
Since DQ is a common side, and triangles DFQ and DPQ share vertex D, we can use the angle addition postulate. This postulate states that the sum of the angles in any triangle is equal to 180 degrees.
3. Solve for angle FQD:
In triangle DFQ, we are given that angle DFQ = 51 degrees. We are also given that angle DPQ = 34 degrees.
Using the angle addition postulate for triangle DFQ:
angle FQD + angle DFQ + angle QDF = 180 degrees
Substituting the known values:
angle FQD + 51 degrees + 34 degrees = 180 degrees
Combining like terms:
angle FQD = 180 degrees - 51 degrees - 34 degrees
Calculating the value of angle FQD:
angle FQD = 95 degrees
Therefore, the measure of angle FQD in the figure is 95 degrees.