Two angles of a quadrilateral measure 85° and 75° respectively.
Question:

Two angles of a quadrilateral measure 85° and 75° respectively. The other two angles are equal. Find the measure of each of these equal angles.

Solution:

Let the two unknown angles measure $x^{\circ}$ each.

Sum of the angles of a quadrilateral is $360^{\circ}$.

$\therefore 85+75+x+x=360$

$160+2 x=360$

$2 x=360-160=200$

$x=100$

Each of the equal angle measures $100^{\circ}$.

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