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3241004551 [841]
3 years ago
6

What is the value of X? show all of your work

Mathematics
1 answer:
Lapatulllka [165]3 years ago
6 0

Answer:

5

Step-by-step explanation:

We need to use Pythagoras' theorem.

For this we can use the pythagoras formula a^2+b^2=c^2 and rearrange this

We then will have 8^2+b^2=89

(because 89(sqrt) squared is 89)

We can then solve for what x is.

We take away 64 from 89 which is 25

the square root of 25 is 5

Therefore x=5

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The measure of the vertex angle is 94 degrees ⇒ A

Step-by-step explanation:

  • In any triangle, the sum of the measures of its interior angle is 180°
  • In the isosceles triangle, the two base angles are equal in measures

∵ In an isosceles triangle, the measure of the base angle = (2x + 5)

∵ The base angles of the isosceles triangles are equal in measures

∴ The measures of the base angles are (2x + 5), (2x + 5)

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∵ The sum of the measure of the three angles = 180°

∴ (2x + 5) + (2x + 5) + (5x - 1) = 180

→ Add the like terms in the left side

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→ Divide both sides by 9 to find x

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→ Substitute the value of x in the measure of the vertex angle to find it

∵ The measure of the vertex angle = 5x - 1

∴ The measure of the vertex angle = 5(19) - 1

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∴ The measure of the vertex angle = 94°

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