Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters
ects a line with points A, D, F at point D. A line extends from point D to point B in between angle A D C. Angle E D F is 120 degrees, angle C D B is (2 x) degrees, and angle B D A is (3 x) degrees. What is the missing reason in step 3? A 2-column table has 9 rows. Column 1 is labeled statements with entries measure of angle E D F = 120 degrees measure of angle A D B = (3 x) degrees measure of angle B D C = (2 x) degrees, angle E D F and angle A D C are vertical angles, angle E D F is-congruent-to angle A D C, measure of angle A D C = measure of angle A D B + measure of angle B D C, measure of angle E D F = measure of angle A D C, measure of angle E D F = measure of angle A D B + measure of angle B D C, 120 = 3 x + 2 x, 120 = 5 x, x = 24. Column 2 is labeled Reasons with entries given, def. of vert. angles, question mark, angle add. post., definition of congruency, substitution, substitution, addition, div, prop. of equality. vertical angles are congruent substitution definition of congruency definition of equality
2 answers:
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.
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Step-by-step explanation:
Let x represent the speed of the first ferry.
Consequently, the second ferry's speed is x-5, as it travels 5 miles per hour slower.
The time taken by the first ferry is calculated as distance divided by speed =
The time taken by the second ferry equals .
Since the second ferry departs one hour earlier, the times differ by 1 hour.
The speed cannot be negative.
Thus, the speed of the first ferry is determined to be 18.5 mph,
and for the second, slower ferry, it equals 13.5 mph.