The second angle of a triangle is 3 times as large as the first. The third angle is 55° more than the first. Find the measure of the smallest angle
x+3x+x+55=180
5x+55=180
5x=125
x=25
25, 75, 80 are the measures of your three angles. I'm sure you can pick out the smallest one.
Let's denote the measure of the first angle as "x".
According to the problem, the second angle is 3 times as large as the first, so it can be expressed as 3x.
The third angle is 55° more than the first, so it can be expressed as x + 55.
Now, we know that the sum of the angles in a triangle is 180°.
So, we can set up an equation:
x + 3x + (x + 55) = 180
Combining like terms:
5x + 55 = 180
Subtracting 55 from both sides:
5x = 125
Dividing both sides by 5:
x = 25
Therefore, the measure of the smallest angle, which is the first angle, is 25°.
To find the measure of the smallest angle, let's denote the measure of the first angle as x.
According to the problem, the second angle is 3 times as large as the first. This means the second angle is 3x.
The third angle is 55° more than the first, so it is x + 55°.
In a triangle, the sum of all angles is always 180°. Therefore, we can write the equation:
x + 3x + (x + 55°) = 180°
Simplifying the equation, we combine like terms:
5x + 55° = 180°
Next, we isolate the variable by subtracting 55° from both sides of the equation:
5x = 180° - 55°
5x = 125°
To solve for x, divide both sides of the equation by 5:
x = 125° / 5
x = 25°
Therefore, the measure of the smallest angle is 25°.