Question

if cdef is a parallelogram, find m∠fcd.
c
d
(10x - 23)°
(5x - 7)°
f
e
x = select
m∠fcd = select °
desmos | graphing calculator | south carolina version

Explanation:

Step1: Use adjacent angles property

In parallelogram, adjacent angles sum to $180^\circ$: $(5x-7)+(10x-23)=180$

Step2: Solve for x

Simplify: $15x-30=180 \Rightarrow 15x=210 \Rightarrow x=14$

Step3: Calculate $\angle FCD$

$\angle FCD=10x-23=10(14)-23=117$

Answer:

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