Find the value of x in each case. give reasons to justify your solutions!

x=27°

Step-by-step explanation:

we know that

The Triangle Exterior Angle Theorem, states that: An exterior angle of a triangle is equal to the sum of the opposite interior angles

step 1

Find the measure of angle PLM

we know that

m∠PLM+m∠LPM=m∠PMN > by Triangle Exterior Angle Theorem

we have

m∠LPM=x°

m∠PMN=2x+72°

substitute

m∠PLM+x=2x+72°

m∠PLM=2x-x+72°

m∠PLM=x+72°

step 2

Find the measure of angle x

we know that

3x+m∠PLM=180° > by supplementary angles (form a linear pair)

we have

m∠PLM=x+72°  (see step 1)

substitute

3x+x+72°=180°

4x=180°-72°

4x=108°

x=27°

26

step-by-step explanation:

step-by-step explanation:

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