The sum of the 3 angles of a triangle is 180 degrees. In triangle PQR, the largest angle is twice the size of the smallest angle. The remaining angle is 16 degrees larger than the smallest. Write and solve an equation to find the size of the smallest angle in degrees.
just put the facts into symbols. Let x be the smallest angle. So, you have
x + (2x) + (x+16) = 180
x = 41
so, the angles are 41, 57, 82
Let's call the smallest angle in triangle PQR "x" degrees.
According to the problem, the largest angle in triangle PQR is twice the size of the smallest angle, so it is 2x degrees.
The remaining angle is 16 degrees larger than the smallest angle, so it is x + 16 degrees.
To find the sum of the angles, we add the three angles together, which should equal 180 degrees:
x + 2x + (x + 16) = 180
Now, we simplify the equation:
4x + 16 = 180
Next, we isolate the variable by subtracting 16 from both sides:
4x = 164
Finally, we solve for x by dividing both sides of the equation by 4:
x = 41
Therefore, the size of the smallest angle in triangle PQR is 41 degrees.
To solve this problem, we can start by assigning variables to the smallest angle, the remaining angle, and the largest angle in the triangle.
Let's say the smallest angle is x degrees. Therefore, the remaining angle is x + 16 degrees, and the largest angle is 2x degrees.
According to the sum of the angles in a triangle (180 degrees), we can write the equation:
x + (x + 16) + 2x = 180
Now, we can solve this equation to find the value of x.
Combining like terms, we have:
4x + 16 = 180
Subtracting 16 from both sides:
4x = 164
Dividing both sides by 4:
x = 41
Therefore, the size of the smallest angle in the triangle is 41 degrees.