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Aleks
20 days ago
5

If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Se

lect all that apply.
A. x=4
B. m<BEG = 72°
C. m<EGC = 120°
D. m<GCB + m<CBE = 180°
E. m<BEG + m<EGC = 230°
F. The sum of all exterior angles of BEGC is equal to 360°.​
Mathematics
1 answer:
Inessa [9K]20 days ago
3 0

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

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h(3k-12.4)

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