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Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x - 10. Find the value of x and then give the measures of all angles of the trapezoid.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
Isosceles trapezoid is a trapezoid whose two opposite sides and two adjacent angles are congruent. If the two adjacent angles of the lower base are congruent, then the two adjacent angles of the upper base are also congruent.
For any trapezoid, the two adjacent sides of a leg are supplementary angles because the upper and lower bases are parallel.
If that's the case, the value of x is
Hence, the measurement of an angle at the lower base of an isosceles trapezoid is
and at the upper base is
Therefore, the measurements of the two congruent angles of an isosceles trapezoid are 77.5° and 102.5°.