The measure of the numbered angles are:
a) m∠1 = 75⁰ b) m∠2 = 35⁰ c) m∠4 = 70⁰
d) m∠6 = 75⁰ e) m∠9 = 70⁰
f) m∠10 = 110⁰ g) m∠12 = 70⁰
h) m∠14 = 75⁰
How the numbered angles are calculated.
From the figure
a||b and m.and l are transversals.
∠7 = 110⁰ and ∠11 = 75⁰
a) ∠1 = ∠11(corresponding ∠s)
∠1 = 75⁰
∠7 + ∠8 = 180(linear angles)
110 + ∠8 = 180
∠8 = 180 - 110
= 70⁰
∠8 + ∠11 + ∠5 =>180(sum of int. ∠s of a ∆)
70 + 75 + ∠5 = 180
∠5 = 180 - 145
∠5 = 35⁰
m∠2 = m∠5(vertical angles)
m∠2 = 35⁰
c) m∠4 = m∠8(alternate interior angles)
m∠4 = 70⁰
d) m∠6 = m∠1(vertical angles)
m∠6 = 75⁰
e) m∠9 = m∠4(corresponding ∠s)
m∠9 = 70⁰
f) m∠10 = m∠7(vertical angles)
m∠10 = 110⁰
m∠12 = m∠4= m∠3(vertical angles and corresp. ∠s)
m∠12 = 70⁰
h) m∠14 = m∠11(vertical angles)
m∠14 = 75⁰