‹RECTANGLE ∥ PARALLELOGRAM›
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[tex]\large\rm{❛PROBLEM❜}[/tex]
- 1.) Given: ABCD is a rectangle. Find the measure of it's diagonal if AC = 4x - 30 and BD = x.
- 2.) Given: STUV is a parallelogram. Find the measure of ∠SVU.
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[tex]\large\rm{❛ANSWER❜}[/tex]
- [tex]\large\rm{1.) \: \: m∠BD \: = \: 10}[/tex]
- [tex]\large\rm{2.) \: m∠SVU \: = \: 124°}[/tex]
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[tex]\large\rm{❛GIVEN❜}[/tex]
- [tex]\small\rm{m∠AC \: = \: 4x - 30}[/tex]
- [tex]\small\rm{m∠BD \: = \: x}[/tex]
- [tex]\small\rm{m∠V \: = \: 12x + 4}[/tex]
- [tex]\small\rm{m∠T \: = \: 13x - 6}[/tex]
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[tex]\large\rm{❛SOLUTION❜}[/tex]
1.) Given: ABCD is a rectangle. Find the measure of it's diagonal if AC = 4x - 30 and BD = x.
↳ We know that opposite sides are congruent so this means.
- [tex]\small\rm{AC \: \cong \: BD}[/tex]
↳ Substitute the given measure.
- [tex]\small\rm{4x \: - \: 30 \: = \: x}[/tex]
↳ Transpose
- [tex]\small\rm{4x \: - \: x \: = \: 30}[/tex]
↳ Divide both sides by 3
- [tex]\small\rm{ \frac{\cancel3x}{ \cancel3} = \frac{30}{3}} \\ [/tex]
- [tex]\small\rm{x \: = \: 10}[/tex]
↳ Since the value of x is 10, now we need to find the measure of it's diagonal so we need to find it by m∠AC and set x to 10.
- [tex]\small\rm{m∠AC \: = \: 4x - 30}[/tex]
- [tex]\small\rm{m∠BD \: = \: 4(10) - 30}[/tex]
- [tex]\small\rm{m∠BD \: = \: 40 - 30}[/tex]
- [tex]\small\rm\color{olive}{m∠BD \: = \: 10}[/tex]
∴ Therefore, the measure of it's 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.
- [tex]\small\rm{m∠V \: \cong \:m∠T}[/tex]
↳ Substitute the given measure.
- [tex]\small\rm{12x + 4 \: = \: 13x \: - \: 6}[/tex]
↳ Transpose
- [tex]\small\rm{12x - 13x \: = \: 4 \: + \: 6}[/tex]
↳ Add and Subtract the given value.
- [tex]\small\rm{1x \: = \: 10}[/tex]
↳ Divide both sides by 1
- [tex]\small\rm{ \frac{\cancel1x}{\cancel1} = \frac{10}{1}} \\ [/tex]
- [tex] \small\rm{x \: = \: 10}[/tex]
↳ Now that we take the value of x, we need to take the m∠V then multiply it and set x to 10.
- [tex]\small\rm{m∠V \: = \: 12x + 4}[/tex]
- [tex]\small\rm{m∠SVU \: = \: 12(10) + 4}[/tex]
- [tex]\small\rm{m∠SVU \: = \: 120 + 4}[/tex]
- [tex]\small\rm\color{olive}{m∠SVU \: = \: 124°}[/tex]
∴ Therefore, the measure angle m∠SVU will be 124°
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[tex]\color{red}{⚘}[/tex]
