Final answer:
To find the value of x and the measure of angle D in triangles TAP and DAN, we can use the given congruence of the triangles and the given angle measures.
Step-by-step explanation:
To find the value of x and the measure of angle D, we need to use the given information that triangle TAP is congruent to triangle DAN.
Since triangle TAP is congruent to triangle DAN, that means angle A is congruent to angle D, angle T is congruent to angle N, and angle P is congruent to angle A.
Given that angle A is 40 degrees and angle N is 60 degrees, we can conclude that angle D is also 40 degrees. To find the value of x, we can use the equation 2x + 10 = 60 and solve for x.
2x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2
x = 25
Therefore, the value of x is 25 and the measure of angle D is 40 degrees.