A quadrilateral has two angles that measure 110° and 120°. The other two angles are in aratio of 6:7. What are the measures of those two angles?andSubmit

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asked Feb 2, 2023 12.4k views

1 Answer

Travis Waelbroeck · Answer 1 · 2023-02-06T14:56:04+0000

From the problem, two angles in a quadrilateral are 110 and 120 degrees.

Note that the sum of interior angles in a quadrilateral is 360 degrees.

Then the sum of the other two angles will be :

And the angles are in a ratio of 6 : 7.

Multiply the ratio by a common factor "x"

$6x\colon7x$

Then take the sum and equate it to 130 degrees.

Solve for x :

$\begin{gathered} 13x=130 \\ x=(130)/(13) \\ x=10 \end{gathered}$

Now, substitute x = 10 to the ratio.

$\begin{gathered} 6(10)\colon7(10) \\ 60\colon70 \end{gathered}$

Therefore, the other two angles are 60 and 70 degrees.

ANSWER :

60 and 70 degrees