Question

find the measures of the numbered angles in the rhombus.
m∠1 = 42°
m∠2 = 90°
m∠3 = 48°
m∠4 = □°

Explanation:

Step1: Use rhombus diagonal properties

Diagonals bisect angles; adjacent angles sum to 180°. Given angle adjacent to 48°: 180°-48°=132°, bisected by diagonal: 132°/2=66°? Wait, no—wait, m∠1=42°, so in the triangle with 48° and ∠4: triangle angles sum to 180°, right angle at ∠2 (diagonals of rhombus are perpendicular, so ∠2=90°).

Step2: Calculate ∠4 in right triangle

Right triangle has angles 90°, 48°, ∠4. So ∠4=180°-90°-48°=42°.

Step3: Verify consistency

∠1=42°, ∠4 should equal ∠1 (diagonals bisect angles, opposite angles' bisectors create equal angles). So ∠4=42°.

Answer:

42