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 =

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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