What is the measure of the smallest angle in the figure? The figure is not drawn to scale.
In this problem my test shows a 90 degree angle, and then for the other two angles, there are algebraic problems. Here are the problems. 6x - 7, and 4x - 3. My answer was 17, but I am so confused and I cannot find the correct value for x.
If someone could answer my question I would be very happy :)
a triangle has a total of 180º
90 + 6x - 7 + 4x - 3 = 180
10x = 100
To find the measure of the smallest angle in the figure, we need to solve for the value of x first.
Given that the two angles are represented by the expressions 6x - 7 and 4x - 3, we can set up an equation using the fact that the sum of the angles in a triangle is 180 degrees.
So, the equation would be:
90 + (6x - 7) + (4x - 3) = 180
Simplifying the equation, we get:
10x + 80 = 180
Next, we isolate the variable by subtracting 80 from both sides of the equation:
10x = 100
Dividing both sides by 10:
x = 10
Now that we have found the value of x, we can substitute it back into the expressions to find the measures of the angles.
The measure of the smallest angle would be:
4x - 3 = 4(10) - 3 = 40 - 3 = 37 degrees
Therefore, the measure of the smallest angle in the figure is 37 degrees.
To find the measure of the smallest angle in the figure, we need to solve for the value of x and substitute it into one of the algebraic expressions provided.
Let's start with the given expressions: 6x - 7 and 4x - 3.
Since the figure is not drawn to scale and we cannot determine the exact measurements of the angles, we'll assume that the 90-degree angle is the largest angle in the figure. This means that the other two angles must be smaller.
To find the value of x, we'll set up an equation based on the fact that the sum of the measures of the three angles in any triangle is always 180 degrees. So, we have:
90 + (6x - 7) + (4x - 3) = 180
Now, let's solve this equation for x.
Combine like terms: 6x + 4x - 7 - 3 = 180
10x - 10 = 180
Next, isolate the variable by adding 10 to both sides of the equation: 10x = 180 + 10
10x = 190
Finally, divide both sides of the equation by 10 to solve for x: x = 190/10
x = 19
Now that we have the value of x, we can substitute it into one of the expressions to find the smallest angle. Let's use 4x - 3:
Smallest angle = 4(19) - 3
Smallest angle = 76 - 3
Smallest angle = 73 degrees
Therefore, the measure of the smallest angle in the figure is 73 degrees.