Question

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​

Answer 1

Explanation:

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

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

`x + x + 75^\circ + 117^\circ = 360^\circ`

Now we can solve for
`x`:

⇒
`2x + 192^\circ = 360^\circ`

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

⇒
`2x = 168^\circ`

⇒
`x = (168^\circ)/(2)` [dividing both sides by 2]

⇒
`x = \bf84^\circ`

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