Question

ex 3
done is an isosceles
trapezoid. $m\angle edo = 110^\circ$
and $m\angle den = (15x - 5)^\circ$.
find the value of x.

Explanation:

Step1: Identify consecutive base angles

In an isosceles trapezoid, consecutive angles between the bases are supplementary. $\angle EDO$ and $\angle DEN$ are consecutive angles along leg $ED$, so:
$$m\angle EDO + m\angle DEN = 180^\circ$$

Step2: Substitute given values

Replace the angles with the provided expressions:
$$110 + (15x - 5) = 180$$

Step3: Simplify and solve for x

Combine like terms and isolate $x$:
$$105 + 15x = 180$$
$$15x = 180 - 105$$
$$15x = 75$$
$$x = \frac{75}{15}$$

Answer:

$x = 5$