Find the value of x in each case. Give reasons to justify your solutions!BRAINLY SHALL BE GIVENL, M ∈ KN 1. m ∠KLP+m∠PLM = __180___ 2. _3x____+m∠PLM = _180_____ Substitution 3. m∠PLM = _______ Algebra 4. m∠PMN=m∠P+m∠______ _______________ 5. ____2x+72__ = _____x_+180°−3x Substitution 6. x= ___27___ Algebra
Accepted Solution
A:
Answer:x=27°Step-by-step explanation:we know thatThe Triangle Exterior Angle Theorem, states that: An exterior angle of a triangle is equal to the sum of the opposite interior anglesstep 1Find the measure of angle PLMwe know thatm∠PLM+m∠LPM=m∠PMN ----> by Triangle Exterior Angle Theoremwe havem∠LPM=x°m∠PMN=2x+72°substitutem∠PLM+x=2x+72°m∠PLM=2x-x+72°m∠PLM=x+72°step 2Find the measure of angle xwe know that3x+m∠PLM=180° ----> by supplementary angles (form a linear pair)we havem∠PLM=x+72° (see step 1)substitute3x+x+72°=180°4x=180°-72°4x=108°x=27°