In the triangle below, suppose that m∠W=(7x-5°), m∠X=(3x-2)°, and =m∠Y=x°
Find the degree measure of each angle in the triangle.
well, the sum of the 3 angles must be 180°, so
7x-5 + 3x-2 + x = 180
11x = 187
x = 17
sub into the definitions to get the angles
Oh, triangles and their angles, they're quite the shape shifters! Let's see what we can do with this one.
We know that the sum of angles in a triangle is always 180°, so we can set up an equation to solve for x:
(7x-5) + (3x-2) + x = 180
Now, let's simplify and solve for x:
11x - 7 = 180
11x = 187
x ≈ 17
Now that we have x, we can plug it back into the equations to find the degree measure of each angle:
∠W = 7x - 5 ≈ 7(17) - 5 ≈ 114°
∠X = 3x - 2 ≈ 3(17) - 2 ≈ 49°
∠Y = x ≈ 17°
So, we have ∠W ≈ 114°, ∠X ≈ 49°, and ∠Y ≈ 17°. Triangle-angle-trouble solved!
To find the degree measure of each angle in the triangle, we can use the fact that the sum of the angles in a triangle is equal to 180 degrees.
Let's find the value of x by adding the degree measures of all three angles and setting it equal to 180 degrees:
m∠W + m∠X + m∠Y = (7x - 5) + (3x - 2) + x
Combine like terms:
11x - 7 = 180
Now, isolate x by adding 7 to both sides:
11x = 187
Divide both sides by 11:
x = 187 / 11
Simplify:
x = 17
Now that we know x, we can substitute it back into the expressions for each angle to find their degree measures:
m∠W = 7x - 5 = 7(17) - 5 = 119 - 5 = 114 degrees
m∠X = 3x - 2 = 3(17) - 2 = 51 - 2 = 49 degrees
m∠Y = x = 17 degrees
Therefore, the degree measure of each angle in the triangle is:
m∠W = 114 degrees
m∠X = 49 degrees
m∠Y = 17 degrees
To find the degree measure of each angle in the triangle, we need to set up an equation using the given information.
In a triangle, the sum of the degree measures of all three angles is always 180 degrees.
So, we can write the equation as:
m∠W + m∠X + m∠Y = 180
Substituting the given expressions for the angles:
(7x - 5) + (3x - 2) + x = 180
Now, we can simplify this equation by combining like terms:
7x + 3x + x - 5 - 2 = 180
Simplifying further:
11x - 7 = 180
Next, we want to solve for x. To do that, we can isolate the variable term:
11x = 180 + 7
11x = 187
Finally, we can solve for x by dividing both sides of the equation by 11:
x = 187/11
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their degree measures.
m∠W = 7x - 5
m∠X = 3x - 2
m∠Y = x
Substituting x = 187/11:
m∠W = 7(187/11) - 5
m∠X = 3(187/11) - 2
m∠Y = 187/11
Simplifying these expressions will give us the degree measures of each angle in the triangle.