Given triangle PQR with m<P=(5x+10) degrees m<Q=(3x+18) degrees and m<R=(2x+32) degrees. Classify triangle PQR by side length and angle measure. Explain your answer
you have, since the angles sum to 180,
5x+10+3x+18+2x+32=180
10x+60=180
10x=120
x=12
Now you can find out the angles, and classify the triangle.
angle subtended by an arc to the center of circle is double the angle subtended by it at any point on the remaining part of the circle
To classify triangle PQR by side length, we need to examine the relationships between the lengths of its sides. However, the information provided in the question does not give us any information about the side lengths, so we cannot determine the classification by side length.
To classify the triangle by angle measure, we need to compare the measures of its angles. Let's start by solving the equations given for each angle:
m<P = 5x + 10
m<Q = 3x + 18
m<R = 2x + 32
To find the values of x and subsequently the measures of each angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the following equation:
m<P + m<Q + m<R = 180
Substituting the equations for the angle measures, we get:
(5x + 10) + (3x + 18) + (2x + 32) = 180
Combining like terms:
10x + 60 = 180
Subtracting 60 from both sides:
10x = 120
Dividing both sides by 10:
x = 12
Now that we know the value of x, we can substitute it back into the equations for each angle:
m<P = 5(12) + 10 = 70 degrees
m<Q = 3(12) + 18 = 54 degrees
m<R = 2(12) + 32 = 56 degrees
Now let's analyze the measure of each angle:
Angle P measures 70 degrees, angle Q measures 54 degrees, and angle R measures 56 degrees.
Based on the measures of the angles, we can classify triangle PQR by angle measure as follows:
- Angle P is the largest, so it is an obtuse angle.
- Angle R is the smallest, so it is an acute angle.
- Angle Q is neither the largest nor the smallest, so it is a non-right angle.
Therefore, triangle PQR is classified by angle measure as an obtuse-angled triangle.