Question

which angles are complementary to each other?
options: ∠3 and ∠2, ∠3 and ∠1, ∠2 and ∠4, ∠1 and ∠4

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Identify right angle marker

$\angle 3$ is marked as a right angle, so $m\angle 3 = 90^\circ$.

Step3: Analyze angle sums

For $\angle 1$ and $\angle 4$: $\angle 3 + \angle 1 + \angle 4 = 180^\circ$ (straight line). Substitute $m\angle 3=90^\circ$:
$90^\circ + m\angle 1 + m\angle 4 = 180^\circ$
$m\angle 1 + m\angle 4 = 90^\circ$
Verify other pairs:

• $\angle3+\angle2=90^\circ+m\angle2>90^\circ$
• $\angle3+\angle1=90^\circ+m\angle1>90^\circ$
• $\angle2+\angle4=m\angle2+m\angle4>90^\circ$ (they form part of a straight line with a right angle)

Answer:

$\angle 1$ and $\angle 4$