If m∠2 = 125°, m∠12 = 37° and m∠18 = 102°, find the measure ∠1 = f.m∠7 = k.m∠13 = b.m∠3 = g.m∠8 = l.m∠14 = c.m∠4 = h.m∠9 = m.m∠15 = d.m∠5 = i.m∠10 = n.m∠16 = e.m∠6 = j.m∠11 = o.m∠17 =
Answers
Answer:
Step-by-step explanation:
1). Since, m∠2 + m∠1 = 180° [Supplementary angles]
125° + m∠1 = 180°
m∠1 = 180° - 125°
m∠1 = 55°
2). Since ∠7 ≅ ∠12 [alternate interior angles]
m∠7 = m∠12 = 37°
3). m∠3 = m∠18 = 102° [Alternate exterior angles]
4). m∠8 + m∠3 + m∠7 = 180°
m∠8 + 102 + 37 = 180
m∠8 = 41°
5). m∠14 = (m∠7 + m∠8) [Alternate angles]
m∠14 = 37 + 41 = 78°
6). m∠4 = 180° - m∠3 [Linear pairs]
= 180 - 102
= 78°
7). m∠9 = m∠3 = 102° [Vertical angles]
8). m∠15 = m∠2 [Alternate exterior angles]
= 125°
9). m∠5 = m∠15 [Corresponding angles]
= 125°
10). m∠10 + m∠5 = 180° [Sum of interior angles on one side of the transversal]
m∠10 = 180 - 125
= 55°
10). m∠16 = m∠10 = 55° [Vertical angles]
11). m∠6 = m∠10 = 55° [Alternate interior angles]
12). m∠11 = m∠15 = 125°
13). m∠17 = m∠14 = 78° [Vertical angles]
The answers are given as follows
Given that
a║b
m∠2 = 125°
m∠12 = 37°
m∠18 = 102°
From the identity of supplementary angles
m∠1 + m∠2= 180°
So m∠1 = 180° - 125° = 55°
m∠7 =m∠12 = 37° (Interior opposite angles )
m∠3 = m∠18=102° (Alternate Exterior angles )
m∠8 = 180° - m∠3 -m∠7 = 180°- 139° = 41°
m∠14 = m∠7+ m∠8= 37° + 41° = 78° ( Alternate opposite angles)
So m∠13 = 180° -78° = 102° (linear pair)
m∠4= 180° - m∠3 = 180° - 102° = 78°
m∠9 =180° - m∠4 = 180° - 78 = 102° (vertically opposite to m∠3)
m∠15 = m∠2 = 125° (Alternate exterior angles)
m∠5 =m∠15 = 125° (Corresponding Angles )
m∠10 = 180° -125° = 55°
m∠16 = m∠10 =55° ( Vertically Opposite Angles)
m∠6 = m∠10 =55° (Alternate interior angles)
m∠11 = 180 ° - m∠6° - m∠7° = 180° - 55° - 37° = 88°
m∠17 = 180° - m∠13 = 180° -102° = 78 °
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