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 congruent " ⇒ 2nd answer
Step-by-step explanation:
* <em>Look to the attached figure </em>
- There are three lines intersected at point D
- We need to find the missing in step 3
∵ Line FA intersects line EC at point D
- The angles formed when two lines cross each other are called
vertical angles
- Vertical angles are congruent (vertical angles theorem)
∴ ∠ADC and ∠FDE are vertical angles
∵ Vertical angles are congruent
∴ ∠EDF ≅ ∠ADC
∴ m∠EDF ≅ m∠ADC
∵ m∠EDF = 120° ⇒ given
∵ m∠ADC = m∠ADB + m∠BDC
∴ m∠ADB + m∠BDC = 120°
∵ m∠ADB = (3x)° ⇒ given
∵ m∠BDC = (2x)° ⇒ given
∴ 3x + 2x = 120 ⇒ add like terms
∴ 5x = 120 ⇒ divide both sides by 5
∴ 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 defin. of vert. ∠s
∠EDF is congruent to ∠ADC vertical angles are
congruent
m∠ADC = m∠ADB + m∠BDC angle add. post.
m∠EDF = m∠ADC defin. of cong.
m∠EDF = m∠ADB + m∠BDC substitution
120° = 3 x + 2 x substitution
120 = 5 x addition
x = 24 division
∴ The missing reason is " vertical angles are congruent "
- From the explanation above ∠ADC and ∠FDE are vertical
angles then they are congruent according to vertical angle
theorem
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