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Inessa [10]
2 years ago
12

Help me please. Find the measures of CAD and DAE

Mathematics
1 answer:
VladimirAG [237]2 years ago
8 0

well, we know the "sum" of both angles is 90°, notice the rectangle in the corner, so we can say that the angles are simply complementary angles, thus

\left( \cfrac{3}{2}x+20 \right)+2x=90\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{3}{2}x+20 + 2x \right)=2(90)} \\\\\\ 3x+40+4x=180\implies 7x+40=180\implies 7x=140\implies x=\cfrac{140}{7} \\\\\\ x = 20~\hfill \stackrel{\measuredangle CAD}{\cfrac{3}{2}20+20\implies 50}\qquad\qquad \stackrel{\measuredangle DAE}{2(20)\implies 40}

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