Question

1. for parallelogram lmno, if (mangle l = 5x - 28) and (mangle n = 3x - 10), find (mangle o).

163
17
173
9

Explanation:

Step1: Use property of parallelogram

In parallelogram $LMNO$, $\angle L$ and $\angle N$ are supplementary, so $m\angle L + m\angle N=180^{\circ}$.
$(5x - 28)+(3x - 10)=180$.

Step2: Combine like - terms

$5x+3x-28 - 10 = 180$, which simplifies to $8x-38 = 180$.

Step3: Solve for $x$

Add 38 to both sides: $8x=180 + 38=218$. Then $x=\frac{218}{8}=\frac{109}{4}=27.25$.

Step4: Find $m\angle N$

Substitute $x = 27.25$ into the formula for $m\angle N$: $m\angle N=3x - 10=3\times27.25-10=81.75 - 10 = 71.75$.

Step5: Find $m\angle O$

$\angle N$ and $\angle O$ are supplementary in parallelogram $LMNO$. So $m\angle O=180 - m\angle N$.
$m\angle O=180-71.75 = 108.25$. But let's check another way using the original equations more carefully.

Back to step 1:
In a parallelogram, adjacent angles are supplementary, so $(5x - 28)+(3x - 10)=180$.
$8x-38 = 180$, $8x=218$, $x=\frac{218}{8}=\frac{109}{4}$.

We know that in parallelogram $LMNO$, $\angle L$ and $\angle O$ are also supplementary.
First, find $x$ from the equation of adjacent - angle sum:
$(5x - 28)+(3x - 10)=180$
$8x-38 = 180$
$8x=218$
$x=\frac{218}{8}=\frac{109}{4}$

$m\angle L=5x - 28=5\times\frac{109}{4}-28=\frac{545}{4}-28=\frac{545 - 112}{4}=\frac{433}{4}=108.25$

$m\angle O = 180 - m\angle L$
$m\angle O=180-(5x - 28)$
Since $(5x - 28)+(3x - 10)=180$, we solve $8x=218$, $x=\frac{109}{4}$
$m\angle L=5\times\frac{109}{4}-28=\frac{545 - 112}{4}=\frac{433}{4}=108.25$
$m\angle O=180 - 108.25 = 173$

Answer:

$173$