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Two angles of a quadrilateral are of measures 75° and 117° respectively and the other two angles are equal find the measure of each of the equal angles​

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saadatk

Answer:

Step-by-step explanation:

The sum of interior angles of a quadrilateral is 360°.

If we consider the measure of one of the unknown angles to be [tex]x[/tex]°, we can set up the following equation:

[tex]x + x + 75^\circ + 117^\circ = 360^\circ[/tex]

Now we can solve for [tex]x[/tex]:

⇒ [tex]2x + 192^\circ = 360^\circ[/tex]

⇒ [tex]2x = 360^\circ - 192^\circ[/tex]        [subtracting 192° from both sides]

⇒ [tex]2x = 168^\circ[/tex]

⇒ [tex]x = \frac{168^\circ}{2}[/tex]                      [dividing both sides by 2]

⇒ [tex]x = \bf84^\circ[/tex]

Therefore, the other two angles each have a measure of 84°.

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