The classification of the angles based on the angle measures and the measure of the angle m∠1, obtained using the relationship between linear pair angles are;
13. ∠1 is an Acute angle
14. ∠2 is an Acute angle
15. ∠BOA is an Obtuse angle
16. C. m∠1 = 128°
What are linear pair angles; Linear pair angles are angles that form a straight line such that when added they have a sum 180°.
The measure of angle 1, m∠1 = 57°, which is an acute angle
The measure of angle 2, m∠2 = 43°, which is an acute angle
Therefore;
13. ∠1 is an acute angle
14. ∠2 is an acute angle
15. m∠BOA = m∠1 + m∠2
Therefore, m∠BOA = 57° + 43°
57° + 43° = 100°
m∠BOA = 100°, which is an obtuse angle
16. The angles (4·x + 16)° and (2·x + 34)° are vertical angles, and we get;
(4·x + 16)° = (2·x + 34)°
4·x - 2·x = 34° - 16°
2·x = 18°
x = 18°/2
x = 9
The angle (2·x + 34) and ∠1 are linear pair angles, therefore, we get;
(2·x + 34) + m∠1 = 180°
(2 × 9 + 34) + m∠1 = 180°
m∠1 = 180° - (2 × 9 + 34)°
180° - (2 × 9 + 34)° = 128°
m∠1 = 128°