Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Given
Normal Hour = 32 hours
Overtime = Hours above 32
Rate for Overtime = 1.4 times normal rate
Earnings = $535.62
Required
Determine the normal hour pay
First, we need to determine the hours worked overtime.
This is:
The equation that binds all the parameters is:
This gives:
Solve for r
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
