Question

in the image below, ∠abc and ∠def are complementary angles. what is the measure of ∠def?

Explanation:

Step1: Recall complementary angles rule

Complementary angles sum to \(90^\circ\). So, \(m\angle ABC + m\angle DEF = 90^\circ\).

Step2: Identify \(m\angle ABC\)

From the diagram, \(m\angle ABC = 38^\circ\).

Step3: Solve for \(m\angle DEF\)

Substitute \(m\angle ABC = 38^\circ\) into the equation: \(38^\circ + m\angle DEF = 90^\circ\). Subtract \(38^\circ\) from both sides: \(m\angle DEF = 90^\circ - 38^\circ = 52^\circ\).

Answer:

\(52^\circ\)