Question

1. find x if m∠1 = 2x + 11 and m∠ywx = 7x - 8.
2. m∠1 = 14x - 1 and m∠2 = 13x + 2. find x.

Explanation:

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Step1: Assume ∠1 and ∠YWX are related

If ∠1 is a part of ∠YWX and assuming ∠1 and ∠YWX are in a ratio - related or equal - related situation (since no other information about their relationship is given, we assume ∠1 is a part of ∠YWX and they are equal). So we set up the equation $2x + 11=7x - 8$.

Step2: Solve for x

Subtract $2x$ from both sides:
$2x+11 - 2x=7x - 8-2x$
$11 = 5x-8$.
Then add 8 to both sides:
$11 + 8=5x-8 + 8$
$19 = 5x$.
Divide both sides by 5:
$x=\frac{19}{5}=3.8$.

Step1: Assume ∠1 and ∠2 are related

If ∠1 and ∠2 are adjacent angles and their sum is a known - angle (since no other information about their relationship is given, we assume they are adjacent and supplementary or equal in some cases. Here, we assume they are equal for simplicity). Set up the equation $14x-1=13x + 2$.

Step2: Solve for x

Subtract $13x$ from both sides:
$14x-1-13x=13x + 2-13x$
$x-1=2$.
Add 1 to both sides:
$x-1 + 1=2 + 1$
$x=3$.

Answer:

$x = 3.8$

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