Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters
Answer:
" Vertical angles are equal " ⇒ 2nd answer
Step-by-step explanation:
* Refer to the attached illustration
- Three lines intersect at point D.
- We have to identify the missing justification in step 3.
∵ Line FA intersects line EC at point D.
- When two lines cross, the angles created are referred to as
vertical angles.
- By the vertical angles theorem, vertical angles are equal.
Thus, ∠ADC and ∠FDE are vertical angles.
Since vertical angles are equal
∴ ∠EDF ≅ ∠ADC
Thus, m∠EDF ≅ m∠ADC
Given that m∠EDF = 120°.
∵ m∠ADC is the sum of m∠ADB and m∠BDC.
Therefore, m∠ADB + m∠BDC = 120°.
∵ m∠ADB = (3x)° ⇒ given.
∵ m∠BDC = (2x)° ⇒ given.
Thus, 3x + 2x = 120 ⇒ combine like terms.
Thus, 5x = 120 ⇒ divide both sides by 5.
Thus, x = 24.
Column (1) Column (2)
m∠EDF = 120° given
m∠ADB = 3 x given
m∠BDC = 2 x given
∠EDF and ∠ADC are vertical angles definition of vertical angles
∠EDF is equal to ∠ADC vertical angles are equal
equal
m∠ADC = m∠ADB + m∠BDC angle addition principle.
m∠EDF = m∠ADC definition of equality.
m∠EDF = m∠ADB + m∠BDC substitution.
120° = 3 x + 2 x substitution.
120 = 5 x addition.
x = 24 division.
∴ The missing justification is " vertical angles are equal "
- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.
