Question

2/2 rectangles, rhombus, squares practice day
solve for x, then solve for m<fcd.

1. if cdef is a parallelogram, find ( mangle fcd ).

( x = )
angle fcd =

Explanation:

Step1: Use consecutive angles property

In a parallelogram, consecutive angles are supplementary, so their sum is $180^\circ$.
$$(10x - 23) + (5x - 7) = 180$$

Step2: Simplify the equation

Combine like terms and solve for $x$.
$$15x - 30 = 180$$
$$15x = 210$$
$$x = \frac{210}{15} = 14$$

Step3: Calculate $m\angle FCD$

Substitute $x=14$ into the expression for $\angle FCD$.
$$m\angle FCD = 10(14) - 23 = 140 - 23 = 117$$

Answer:

$x = 14$
angle FCD = $117^\circ$