Question 117

Two straight parallel lines are cut by a transversal, such that, the measures of two co-interior angles are $$\frac{3x}{4}$$ and $$\left(\frac{5x}{4} - 20 \right)$$. What are the values of the measures of the two angles (in $$^\circ$$), respectively?

Solution

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The sum of two co-interior angles in the same side shall add up to 180$$^\circ$$.

Hence, $$\frac{3x}{4}$$+$$\left(\frac{5x}{4} - 20 \right)$$ = 180

Or 8x = 800, making x = 100

Hence, $$\frac{3x}{4}$$ = 75 and $$\left(\frac{5x}{4} - 20 \right)$$ = 105

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