Question : In the following figure, if l || m, then find the measures of angles marked by a and b.
Option 1: a = 90$^{\circ}$ and b = 90$^{\circ}$
Option 2: a = 55$^{\circ}$ and b = 125$^{\circ}$
Option 3: a = 70$^{\circ}$ and b = 110$^{\circ}$
Option 4: a = 60$^{\circ}$ and b = 120$^{\circ}$
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Correct Answer: a = 70$^{\circ}$ and b = 110$^{\circ}$
Solution :
Since $l \parallel m$,
⇒ $\angle$ c = 110$^{\circ}$ (corresponding angles are equal)
Also, $\angle$ a + $\angle$ c = 180$^{\circ}$ (supplementary angles)
⇒ $\angle$ a = 180$^{\circ}$ – 110$^{\circ}$ = 70$^{\circ}$
Now, $\angle$ b = $\angle$ a + 40$^{\circ}$ (exterior angle of a triangle)
= 70$^{\circ}$ + 40$^{\circ}$
= 110$^{\circ}$
Hence, the correct answer is a = 70$^{\circ}$ and b = 110$^{\circ}$.
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