Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that
is 135 degrees. Angle C A B is 75 degrees. What is m∠ABC? M∠ABC = 15° m∠ABC = 45° m∠ABC = 60° m∠ABC = 75°
2 answers:
Answer:
m∠ABC = 45°
Step-by-step explanation:
See the attached figure.
As shown in the figure
Line C B extends through point D to form the exterior angle that is 135 degrees.
So, m∠ABD = 135°
But m∠ABC + m∠ABD = 180°
∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°
Also, we should know that
m∠ABD = m∠BAC + m∠ACB
So, m∠ACB = 135° - 75° = 60°
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<u>Very important note:</u>
If we replaced the location of B and C
SO, m∠ABC = 60° and m∠ACB = 45°
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Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: cos 2A = 2cos²A - 1
Use the Difference Identity: cos (A - B) = cosA · cosB + sinA · sinB
Use the Unit Circle to evaluate: cos (π/2) = 0 & sin (π/2) = 1
<u>Proof LHS → RHS</u>
LHS = RHS: sin A = sin A
Answer:
40 shares each and $3,000 each
Step-by-step explanation:
The computation is shown below:
For the number of shares
Since there are total of 500 shares out of which 260 shares are held by Caren so the remaining shares left is
= 500 shares - 260 shares
= 240 shares
And, there are 6 investors
So the number of shares owned by each investor is
= 40 shares
Now the value of the shares held by each inventory is
= $3,000
Total debt is $65,000
So, the liability per share is
= $130
And each investor holds 40 shares
So, each investor is liable for
= $5,200
As we can see that the value of the shares is less than the amount liable by each investor
So each investor is liable for $3,000
And, the liability of Caren is
= $19,500