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# rhombus

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In  In rhombus ZABC, if angle ZAC = 23, find angle ABZ.

Apr 2, 2021

#1
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Because line AC splits angle ZAB into two equal angles, so ZAC=23, then ZAB=46. But because ZAB is a half of a rhombus, ABZ and AZB must be equal. Let's denote them: \$x\$. We have x+x+46=180, which gives 2x+46=180, which gives 2x=134, which gives \$\boxed{x=ABZ=67^\circ}\$

Apr 2, 2021
edited by RiemannIntegralzzz  Apr 2, 2021
#2
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If ZAC = 23 that means CAB = 23 and we see there is a triangle and more importantly it is a Right triangle so that means 90+23 = 113 and we know that the angles of a triangle are equal to 180 meaning our equation is 180 - 113 = 67 degrees

Apr 2, 2021
edited by itachiuchihakujo  Apr 2, 2021