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In the diagram above, l1 is parallel to l2, Find the value of < PMT...

Question

In the diagram above, l1 is parallel to l2, Find the value of < PMT

A) 82o

B) 36o

C) 72o

D) 118o

Explanation:

< MPT = $$180^{\circ}$$ - $$118^{\circ}$$ = $$62^{\circ}$$
< PML = $$62^{\circ}$$ (Alternating angles)
y + 2y + $$10^{\circ}$$ + $$62^{\circ}$$ = $$180^{\circ}$$ (Angles on a straight line)
3y = 180 - 72
$$\cfrac{3y}{3}$$ = $$\cfrac{108}{3}$$
y = $$36^{\circ}$$
< PMT = 2y + 10 = 2(36) + 10 = $$82^{\circ}$$

Dicussion (1)

• < MPT = $$180^{\circ}$$ - $$118^{\circ}$$ = $$62^{\circ}$$
< PML = $$62^{\circ}$$ (Alternating angles)
y + 2y + $$10^{\circ}$$ + $$62^{\circ}$$ = $$180^{\circ}$$ (Angles on a straight line)
3y = 180 - 72
$$\cfrac{3y}{3}$$ = $$\cfrac{108}{3}$$
y = $$36^{\circ}$$
< PMT = 2y + 10 = 2(36) + 10 = $$82^{\circ}$$