Question

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2. In the figure, AB and CD are parallel lines intersected by a
transversal PQ at points L and M respectively.
IF _PLB = 45° find the measure of all other angles.​

Answer 1

Answer:

angles 2, 3, 6 and 7 are all 45 deg

and angles 1, 4, 5, 8 are 135 degrees.

hope it helps!!!

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thanks!

attachment given for reference (given numbers for each angle)

Explaination:  

if the transversal cuts them at the given points, the following properties are observed:

• corresponding angles are equal.
• adjacent angles' sum is 180 deg

using these two, we can find out all the angles.

we need to find the angle of _PLA, which is 180 - 45 = 135 deg

because these angles are equal, we can tell the measure of each angle.

• angles 1, 4, 5 and 8 are equal.
• angles 2, 3, 6 and 7 are also equal.

so, we can tell that angles 2, 3, 6 and 7 are all 45 deg

and angles 1, 4, 5, 8 are 135 degrees.