Answer:
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)
∵ The measure of the vertex angle = (5x - 1)
∵ 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
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ 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
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
Answer:
{36, 66, 78}
Step-by-step explanation:
Let the measures of the three angles be f, s and t, for first, second and third. Then s + t = 4f, t = 12 + s, and f + s + t = 180.
Subbing 12 + s for t in the first equation, we get s + 12 + s = 4f.
Subbing the same in the third equation, we get f + s + 12 + s = 180
This results in two equations in two unknowns (f and s):
2s - 4f = -12
2s + f = 168.
Let's eliminate s by subtracting the first of these two equations from the second. Doing so yields 5f = 180. Then the first angle, f, or x, is 36.
Then, from 2s + f = 168, we get 2s + 36 = 168, or 2s = 132. Thus, the second angle is s = y = 66.
The sum of the three angles must be 180. Thus, 36 + 66 + t = 180, or
102 + t = 180, or t = z = 78.
The three angles are
{36, 66, 78}.
Answer:
x + 5 + x + 5
5 + 5 + x + x
Step-by-step explanation:
It’s b hope you get a good grade on the test
Meriden would need 2 1/4 cups of sugar because 3*3/4=2 1/4