Question

what is the value of a?
f
c
d
2a
a+30°
e
a = □°

Explanation:

Step1: Use the property of congruent triangles

Since \(FC = FE\) (marked equal), \( \angle FCD=\angle FED = 90^{\circ}\), and \(FD = FD\) (common side), by the Hypotenuse - Leg (HL) congruence criterion, \(\triangle FCD\cong\triangle FED\). Then \(\angle CDF=\angle EDF\).

Step2: Set up the equation

We know that \(2a=a + 30^{\circ}\).
Subtract \(a\) from both sides of the equation: \(2a-a=a + 30^{\circ}-a\).

Answer:

\(30\)