Based on the diagram, we can identify two pairs of supplementary angles: ∠1 and ∠3, and ∠2 and ∠4. Supplementary angles are two angles that add up to 180°.Therefore, the measures of all the angles in the diagram are ∠1 = 21°, ∠2 = 21°, ∠3 = 159°, and ∠4 = 159°.
To solve for the measures of all the angles in the diagram, we can utilize the given information that m/2 = 159°. Based on the diagram, we can identify two pairs of supplementary angles: ∠1 and ∠3, and ∠2 and ∠4. Supplementary angles are two angles that add up to 180°.
Using the given information, we can determine the measure of ∠4: m∠4 = 159°
Since ∠1 and ∠3 are supplementary angles, we can set up the equation:
m∠1 + m∠4 = 180°
Substituting the known value of m∠4, we get m∠1 + 159° = 180°
Solving for m∠1, we find m∠1 = 21°
Similarly, we can determine the measure of ∠2: m∠2 + m∠4 = 180°
Substituting the known value of m∠4, we get m∠2 + 159° = 180°
Solving for m∠2, we find m∠2 = 21°
Therefore, the measures of all the angles in the diagram are ∠1 = 21°, ∠2 = 21°, ∠3 = 159°, and ∠4 = 159°.