Question

1. if m∠ deg = 95, find m∠ def and m∠ feg

x =

m∠ def =

m∠ feg =

(diagram: at point e, there are rays ed, ef, eg, eh. ∠def is (x+5)°, ∠feg is x°, and ∠deg is 95°)

Explanation:

Step1: Set up angle sum equation

$\angle DEF + \angle FEG = \angle DEG$
$(x+5) + x = 85$

Step2: Solve for $x$

Combine like terms: $2x + 5 = 85$
Subtract 5: $2x = 80$
Divide by 2: $x = 40$

Step3: Calculate $m\angle DEF$

Substitute $x=40$: $m\angle DEF = 40 + 5 = 45$

Step4: Calculate $m\angle FEG$

$m\angle FEG = x = 40$

Answer:

$x = 40$
$m\angle DEF = 45^\circ$
$m\angle FEG = 40^\circ$