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Crank
3 years ago
7

What is the value of k?​

Mathematics
2 answers:
iragen [17]3 years ago
8 0

Answer:

(4k+5)+ (6k+10) = 115

Exterior angle of a triangle is equal to the sum of two opposite interior angles

10k=15=115

10k= 100

k = 100/10

k = 10

Step-by-step explanation:

REY [17]3 years ago
8 0

Answer:

k = 10

Step-by-step explanation:

The 3rd angle that's not defined in the equation is supplementary to 115, so the angle is 180-115 = 65.

We can solve for the equation 65+(4k+5)+(6k+10)=180 -> 65+4k+5+6k+10=180 -> 10k+80 = 180 -> 10k = 100 -> k = 10.

To double-check(optional), we can plug k back into the equation, so 65 + 4*10 + 5 + 6*10 + 10 = 180 -> 100 + 65 + 5 + 10 = 180 -> 180 = 180, so we can confirm that k = 10.

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3 years ago
Solve the following using completing the square method :
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For the rhombus below, find the measure of angles 1,2,3 and 4.
Alexus [3.1K]

Answer:

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Step-by-step explanation:

First off, we already know that ∠2 is 57° because of alternate interior angles.

Second, it's important to know that rhombus' diagonals bisect each other; meaning they form 90° angles in the intersection. Another cool thing is that the diagonals bisect the existing angles in the rhombus. Therefore, 57° is just half of something.

Then, you basically just do some other pain-in-the-butt things after.

Since that ∠2 is just the bisected half from one existing angle, that means that ∠3 is just the other half; meaning that ∠3 is 57°, as well.

Next is to just find the missing angle ∠1. Since we already know ∠3 is 57°, we can just add that to the 90° that the diagonals formed at the intersection.

57° + 90° = 147°

180° - 147° = 33°

∠1 is 33°

Finally, since that ∠4 is just an alternate interior angle of ∠1, ∠4 is 33°, too.

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3 years ago
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