Question

Please help

1. If m∠5 = 42° and m∠1 = 117°, find m∠CDF.
2. Question 7 options:
If m∠3=73° and DG−→−⊥DF−→− find m∠FDE
3. In the diagram below, BC−→− bisects ∠FBE
If m∠ABF=(7x+20)°, m∠FBC=(2x−5)° and m∠ABC=159°, find the value of x.
4. In the diagram below, BC−→− bisects ∠FBE
If m∠DBC=(12x−3)°, m∠DBE=(5x+12)°, and m∠EBC=(3x+13)°, find m∠EBC
5. In the diagram below, BC−→− bisects ∠FBE
If m∠FBC=(10x−9)°, m∠CBE=(4x+15)°,find m∠FBE.

Answer 1

• See below

Explanation:

#1

• m∠CDF = m∠5 + m∠1 = 42° + 117° = 159°

#2

• m∠FDE = m∠FDG - m∠3 = 90° - 73° = 17°

#3

m∠ABC = m∠ABF + ∠mFBC

• 159 = 7x + 20 + 2x - 5
• 159 = 9x + 15
• 9x = 159 - 15
• 9x = 144
• x = 144/9
• x = 16

#4

m∠EBC = m∠DBC - m∠DBE

• 3x + 13 = 12x - 3 - 5x - 12
• 3x + 13 = 7x - 15
• 7x - 3x = 13 + 15
• 4x = 28
• x = 7

m∠EBC = 3*7 + 13 = 21 + 13 = 34°

#5

m∠FBE = m∠FBC + m∠CBE and m∠FBC = m∠CBE

m∠FBE = 2m∠CBE

• 10x - 9 = 4x + 15
• 10x - 4x = 15 + 9
• 6x = 24
• x = 4

m∠FBE = 2*(4*4 + 15) = 2*31 = 62°