Two angles are congruent and complementary. what is the measure of each angle?

a) 45°
b) 90°
c) 180°
d) the measure of each angle cannot be determined.

 The correct option is (A) 45°.

Step-by-step explanation:  Given that two angles are congruent and complementary.

We are to find the measure of each angle.

Since the angles are congruent, so their measures must be equal.

Let x° be the measure of each of the two angles.

We know that

the sum of the measurements of two complementary angles is 90°, so we must have

Thus, the measure of each of the angles is 45°.

Option (A) is CORRECT.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.