Answer:
The total of all exterior angles in BEGC equals 360° ⇒ only answer F is correct
Step-by-step explanation:
* Let’s review some basics regarding quadrilaterals
- A quadrilateral is a polygon that has four sides
- The interior angles of any quadrilateral add up to 360°
- The exterior angles of any quadrilateral also total 360°
* Now let’s tackle the problem
- DEGC is indeed a quadrilateral
∵ m∠BEG = (19x + 3)°
∵ m∠EGC = (m∠GCB + 4x)°
∵ The total of the interior angles measures 360°
∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360
∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ combine like terms
∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ subtract 3 from both sides
∴ 23x + 2m∠GCB + m∠CBE = 375
∵ The exterior angles of any quadrilateral will always sum to 360°
∴ Only the statement in answer F holds true