Question

you have information about 3 angle pairs. use this information to find the measure of angle a.
now you know that angle e has a measure of 45°. the last clue tells you that angle a and angle e are complementary angles. use this to find the measure of angle a.
angles c and d are supplementary angles.
angles c and e are vertical angles.
angles a and e are complementary angles.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). So, if \(a\) and \(e\) are complementary, then \(a + e=90^{\circ}\).

Step2: Substitute the value of \(e\)

Given \(e = 45^{\circ}\), substitute into the equation \(a+e = 90^{\circ}\). We get \(a+45^{\circ}=90^{\circ}\).

Step3: Solve for \(a\)

Subtract \(45^{\circ}\) from both sides of the equation: \(a=90^{\circ}-45^{\circ}\).

Answer:

\(45^{\circ}\)