Answer:
Step-by-step explanation:
Given m∠3 = 54°
a). m∠1 + m∠2 + m∠3 = 180° [Linear angles]
m∠1 + 90° + 54° = 180°
m∠1 = 180° - 144°
= 36°
b). m∠2 = 90° [Given]
c). m∠4 = m∠1 [Vertically opposite angles]
m∠4 = 36°
d). m∠2 = m∠5 = 90° [Vertically opposite angles]
e). m∠3 = m∠6 = 54° [Vertically opposite angles]
f). m∠7 = m∠1 + m∠2 [Corresponding angles]
= 36° + 90°
= 126°
g). m∠8 = 180° - m∠7 [Linear pair of angles]
= 180° - 126°
= 54°
h). m∠9 = m∠7 = 126° [[Vertically opposite angles]
i). m∠10 = m∠8 = 54° [Vertically opposite angles]
j). m∠11 = m∠1 = 36° [Corresponding angles]
k). m∠12 = m∠3 + m∠2 = 54° + 90° [Corresponding angles]
= 145°
l). m∠13 = m∠11 = 36° [Vertically opposite angles]
m). m∠14 = m∠5 + m∠6
= 90° + 54°
= 145°
