Find the value of x.
A triangle is shown with 2 congruent sides. One base angle opposite of a congruent side is labeled left parenthesis 5 x right parenthesis degrees. The other base angle opposite of the other congruent side is labeled left parenthesis 3 x plus 28 right parenthesis degrees.
(1 point)
Responses
14
14
20
20
12
12
19
Based on the given information, we can set up the equation:
5x + 3x + 28 = 180
Combining like terms, we get:
8x + 28 = 180
Subtracting 28 from both sides:
8x = 152
Dividing both sides by 8:
x = 19
Therefore, the value of x is 19.
To find the value of x, we will set up an equation by using the properties of a triangle.
In a triangle, the sum of all angles is 180 degrees.
The given triangle has two congruent sides, which means the base angles are equal.
Let's set up the equation:
(5x) + (3x + 28) + (3x + 28) = 180
Now, simplify the equation:
5x + 3x + 28 + 3x + 28 = 180
Combine like terms:
11x + 56 = 180
Next, isolate the variable by subtracting 56 from both sides:
11x = 180 - 56
11x = 124
Finally, solve for x by dividing both sides by 11:
x = 124/11
x = 11.27 (rounded to two decimal places)
Therefore, the value of x is approximately 11.27.
To find the value of x in this triangle, we need to use the fact that the sum of the three angles in a triangle is always 180 degrees.
Let's start by labeling the three angles in the triangle:
- The base angle opposite to the 2 congruent sides is labeled (5x) degrees.
- The other base angle opposite the other congruent side is labeled (3x + 28) degrees.
Since we know that the sum of these three angles is 180 degrees, we can set up the equation:
(5x) + (3x + 28) + (the third angle) = 180
Simplifying the equation:
8x + 28 + (the third angle) = 180
To solve for x, we need to find the value of (the third angle).
Since we know that the triangle has two congruent sides, the third angle is equal to the base angle opposite the remaining congruent side.
Therefore, the third angle is also (5x) degrees.
Substituting (5x) for (the third angle) in the equation:
8x + 28 + 5x = 180
Combining like terms:
13x + 28 = 180
Now, let's isolate the variable x by subtracting 28 from both sides of the equation:
13x = 180 - 28
13x = 152
Finally, we can solve for x by dividing both sides of the equation by 13:
x = 152 / 13
Using long division:
13 | 152
- 143
---
90
- 78
---
120
- 117
----
30
Dividing 152 by 13 results in a quotient of 11 with a remainder of 9.
Therefore, x is approximately 11 remainder 9, or x ≈ 11.692.
So, the value of x in this triangle is approximately 11.692.