Question

which pair of angles x and y are supplementary?\
\\( m\angle x = 76 \\)\
\\( m\angle y = 14 \\)\
\\( m\angle x = 140 \\)\
\\( m\angle y = 190 \\)\
\\( m\angle x = 180 \\)\
\\( m\angle y = 180 \\)\
\\( m\angle x = 113 \\)\
\\( m\angle y = 67 \\)\
\\( \overleftrightarrow{ab} \\) and ( \overleftrightarrow{cd} ) intersect at point e, ( m\angle aec = 6x + 20 ), and ( m\angle deb = 10x ).\
what is the value of x?\
\\( 4\frac{3}{8} \\)\
\\( 21\frac{1}{4} \\)\
10\
5

Explanation:

First Question:

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Test Option 1

$76 + 14 = 90
eq 180$

Step3: Test Option 2

$140 + 190 = 330
eq 180$

Step4: Test Option 3

$180 + 180 = 360
eq 180$

Step5: Test Option 4

$113 + 67 = 180$

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Second Question:

Step1: Identify vertical angles

$\angle AEC$ and $\angle DEB$ are vertical angles, so they are congruent.

Step2: Set up equation

$6x + 20 = 10x$

Step3: Solve for $x$

$20 = 10x - 6x$
$20 = 4x$
$x = \frac{20}{4} = 5$

Answer:

$m\angle x = 113$, $m\angle y = 67$