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‹RECTANGLE ∥ PARALLELOGRAM›

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$\large\rm{❛PROBLEM❜}$

1.) Given: ABCD is a rectangle. Find the measure of its diagonal if AC = 4x – 30 and BD = x.

2.) Given: STUV is a parallelogram. Find the measure of ∠SVU.

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$\large\rm{❛ANSWER❜}$

$\large\rm{1.) \: \: m∠BD \: = \: 10}$

$\large\rm{2.) \: m∠SVU \: = \: 124°}$

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$\large\rm{❛GIVEN❜}$

$\small\rm{m∠AC \: = \: 4x - 30}$

$\small\rm{m∠BD \: = \: x}$

$\small\rm{m∠V \: = \: 12x + 4}$

$\small\rm{m∠T \: = \: 13x - 6}$

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$\large\rm{❛SOLUTION❜}$

1.) Given: ABCD is a rectangle. Find the measure of its diagonal if AC = 4x – 30 and BD = x.

↳ We know that opposite sides are congruent so this means.

$\small\rm{AC \: \cong \: BD}$

↳ Substitute the given measure.

$\small\rm{4x \: - \: 30 \: = \: x}$

↳ Transpose

$\small\rm{4x \: - \: x \: = \: 30}$

↳ Divide both sides by 3

$\small\rm{ \frac{\cancel3x}{ \cancel3} = \frac{30}{3}} \\$

$\small\rm{x \: = \: 10}$

↳ Since the value of x is 10, now we need to find the measure of its diagonal so we need to find it by m∠AC and set x to 10.

$\small\rm{m∠AC \: = \: 4x - 30}$

$\small\rm{m∠BD \: = \: 4(10) - 30}$

$\small\rm{m∠BD \: = \: 40 - 30}$

$\small\rm\color{olive}{m∠BD \: = \: 10}$

∴ Therefore, the measure of its diagonal is 10.

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2.) Given: STUV is a parallelogram. Find the measure of ∠SVU.

↳ We know that opposite sides are congruent so this means.

$\small\rm{m∠V \: \cong \:m∠T}$

↳ Substitute the given measure.

$\small\rm{12x + 4 \: = \: 13x \: - \: 6}$

↳ Transpose

$\small\rm{12x - 13x \: = \: 4 \: + \: 6}$

↳ Add and Subtract the given value.

$\small\rm{1x \: = \: 10}$

↳ Divide both sides by 1

$\small\rm{ \frac{\cancel1x}{\cancel1} = \frac{10}{1}} \\$

$\small\rm{x \: = \: 10}$

↳ Now that we take the value of x, we need to take the m∠V then multiply it and set x to 10.

$\small\rm{m∠V \: = \: 12x + 4}$

$\small\rm{m∠SVU \: = \: 12(10) + 4}$

$\small\rm{m∠SVU \: = \: 120 + 4}$

$\small\rm\color{olive}{m∠SVU \: = \: 124°}$

∴ Therefore, the measure angle m∠SVU will be 124°

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$\color{red}{⚘}$

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‹RECTANGLE ∥ PARALLELOGRAM›

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