Show all work and explain in wordsFindthe value of x. Then find the measure of each labeled angle.

Accepted Solution

Answer:Part 5) [tex]x=50\°[/tex]Part 6) [tex]x=15\°[/tex]Step-by-step explanation:Part 5) we know that[tex](2x-10)\°+90\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)solve for x[tex]2x=180\°-80\°[/tex][tex]2x=100\°[/tex][tex]x=50\°[/tex]Find the value of the labeled angle[tex](2x-10)\°=2(50\°)-10\°=90\°[/tex] ----> is a right angleVerify the answerwe know thatIn a quadrilateral the sum of the internal angles must be equal to 360 degrees so[tex](2x-10)\°+90\°+(180-x)\°+x\°=360\°[/tex][tex](2x+260)\°=360\°[/tex]substitute the value of x[tex]2(50\°)+260\°=360\°[/tex][tex]360\°=360\°[/tex] ------> is true, therefore the value of x is correctPart 6) we know that[tex](8x+10)\°+(4x-10)\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)solve for x[tex]12x=180\°[/tex][tex]x=15\°[/tex]Find the value of each labeled angle[tex](8x+10)\°=8(15\°)+10\°=130\°[/tex] [tex](4x-10)\°=4(15\°)-10\°=50\°[/tex] [tex]130\°[/tex] and [tex]50\°[/tex] are supplementary angles