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Luke has a quadrilateral garden. Upon examining the lot, he found out the four corners had a ratio of 3:4:8:9 respectively. What are the measures of the four corners?

A. 45:60:120:135
B. 50:65:115:130
C. 55:70:110:125
D. 60:75:105:120​


Sagot :

Answer:

A. 45:60:120:135

Step-by-step explanation:

The sum of all angles in a quadrilateral garden are 360 degrees. Let the ratio of four corners are 3x, 4x, 8x, and 9x respectively.

[tex]\begin{gathered}\boxed{\begin{array}{l} \ \ \rm \angle A : \angle B : \angle C : \angle D = 360 \degree \\ \rm \angle A + \angle B + \angle C + \angle D = 360 \degree \\ \ \ \ \rm 3x + 4x + 8x + 9x = 360 \\ \quad \quad \quad \ \rm 24x = 360 \degree \\ \quad \quad \quad \ \rm \large x = \frac{(360 \degree)}{24} \\ \quad \quad \quad \ \ \ \rm x = 15 \degree\end{array}}\end{gathered}[/tex]

Then, let's find the measure of all corners

  • [tex]\begin{gathered} \rm 3x = 3(15 \degree) = 45 \degree \end{gathered}[/tex]

  • [tex]\begin{gathered} \rm 4x = 4(15 \degree) = 60 \degree \end{gathered}[/tex]

  • [tex]\begin{gathered} \rm 8x = 8(15 \degree) = 120 \degree \end{gathered}[/tex]

  • [tex]\begin{gathered} \rm 9x = 9(15 \degree) = 135 \degree \end{gathered}[/tex]