Question

3 use the figure below to answer the questions. find the measure of each angle, then classify it as acute, right, obtuse, or straight.
$m\angle axb =$
$m\angle dxa =$
$m\angle axg =$
$m\angle bxf =$
$m\angle cxg =$
$m\angle fx c =$
$m\angle cxd =$
$m\angle exa =$

Explanation:

Step1: Measure ∠AXB

Ray XA aligns with 0°, ray XB aligns with 50°.
$m\angle AXB = 50^\circ - 0^\circ = 50^\circ$
Classify: Acute (0° < 50° < 90°)

Step2: Measure ∠DXA

Ray XA aligns with 0°, ray XD aligns with 90°.
$m\angle DXA = 90^\circ - 0^\circ = 90^\circ$
Classify: Right (90° exactly)

Step3: Measure ∠AXG

Ray XA aligns with 0°, ray XG aligns with 180°.
$m\angle AXG = 180^\circ - 0^\circ = 180^\circ$
Classify: Straight (180° exactly)

Step4: Measure ∠BXF

Ray XB aligns with 50°, ray XF aligns with 140°.
$m\angle BXF = 140^\circ - 50^\circ = 90^\circ$
Classify: Right (90° exactly)

Step5: Measure ∠CXG

Ray XC aligns with 70°, ray XG aligns with 180°.
$m\angle CXG = 180^\circ - 70^\circ = 110^\circ$
Classify: Obtuse (90° < 110° < 180°)

Step6: Measure ∠FXC

Ray XF aligns with 140°, ray XC aligns with 70°.
$m\angle FXC = 140^\circ - 70^\circ = 70^\circ$
Classify: Acute (0° < 70° < 90°)

Step7: Measure ∠CXD

Ray XC aligns with 70°, ray XD aligns with 90°.
$m\angle CXD = 90^\circ - 70^\circ = 20^\circ$
Classify: Acute (0° < 20° < 90°)

Step8: Measure ∠EXA

Ray XE aligns with 120°, ray XA aligns with 0°.
$m\angle EXA = 120^\circ - 0^\circ = 120^\circ$
Classify: Obtuse (90° < 120° < 180°)

Answer:

1. $m\angle AXB = 50^\circ$, Acute
2. $m\angle DXA = 90^\circ$, Right
3. $m\angle AXG = 180^\circ$, Straight
4. $m\angle BXF = 90^\circ$, Right
5. $m\angle CXG = 110^\circ$, Obtuse
6. $m\angle FXC = 70^\circ$, Acute
7. $m\angle CXD = 20^\circ$, Acute
8. $m\angle EXA = 120^\circ$, Obtuse