Question

1. find the measurement indicated. find ( mangle dec )

image of a parallelogram - like figure with points d, c, f, e; angle at d is ( 75^circ ), angle ( angle dec ) is ( 7x - 5 ), angle ( angle fec ) is ( 15x )
type a response

Explanation:

Step1: Identify parallel line angles

Since $EF \parallel DC$, $\angle FEC = \angle DCE = 15x$ (alternate interior angles).

Step2: Use triangle angle sum rule

In $\triangle DEC$, sum of angles is $180^\circ$:
$$75^\circ + (7x-5) + 15x = 180^\circ$$

Step3: Simplify and solve for $x$

Combine like terms:
$$70 + 22x = 180$$
$$22x = 110$$
$$x = 5$$

Step4: Calculate $m\angle DEC$

Substitute $x=5$ into $7x-5$:
$$7(5)-5 = 35-5 = 30$$

Answer:

$30^\circ$