Question

Im comfused need help

Answer 1

5) So for parallelogram ABCD, ∠B ≅ ∠D, and ∠A ≅ ∠C. Further, ∠B and ∠A are supplementary (i.e., their sum is 180°), and ∠D and ∠C are also supplementary.

So, we have that m∠B = m∠D. Therefore, 

$6x-42=3x+15\\3x=57\\x=19$.

Now, let's substitute for x back into the expression for either ∠B or ∠D to find it's angle measure.

m∠B = $6(19)-42=72$

Now, remember that ∠B or ∠D are supplements of ∠A. 

So, m∠B + m∠A = 180°.

That means m∠A = 180° – 72° = 108°.

That seems reasonable, because A appears to be an obtuse angle.

6) 

m∠BAE + m∠DAE + m∠ABC = 180°
$3x+6+10x+2+12x-3=180\\25x+5=180\\x=7$

∠ABC ≅ ∠ADC.

m∠ABC = $12(7)-3=81$

m∠ADC = 81°.

7)

$AC=5x+1$
$AE=3x-3$
$AB=4x+1$

$AC=2AE\\\\5x+1=2(3x-3)\\\\5x+1=6x-6\\\\7=x$

$AB=DC$

$AB=4(7)+1=29$

DC = 29