The ratio of two angles of a triangle is 3:2.The remaining angle is the smallest which is half the largest
angle of the triangle. What is the measure of smaller angle of a parallelogram if sum of both smaller angles
of the triangle is equal to the larger angle of the parallelogram?
3 x + 2 x + (3/2) x = 180
now try
Oh, and remember that sum of angles in parallelogram is 360
The angles of a triangle are in the ratio 2 6 7 the complement of the smallest
The angles of a triangle are in the ratio of 2:6:7.the complement of the smallest angle of the triangle is
To find the measure of the smaller angle of the parallelogram, let's first determine the measures of the angles in the triangle.
Let's assume that the two angles in the triangle have a ratio of 3:2. We can assign variables to these angles. Let's call one angle 3x and the other angle 2x.
According to the given information, the remaining angle in the triangle is the smallest and is half the largest angle.
Let's say the largest angle in the triangle is 3x. Therefore, the smallest angle is (1/2) * 3x, which simplifies to (3/2)x.
The sum of all angles in a triangle is 180 degrees. So, we can set up an equation:
3x + 2x + (3/2)x = 180
Combine like terms:
(13/2)x = 180
Multiply both sides of the equation by (2/13) to solve for x:
x = (180 * 2) / 13
x ≈ 27.692
Now that we have the value of x, we can find the measures of the two smaller angles in the triangle:
Smaller angle 1 = (3/2)x = (3/2) * 27.692 ≈ 41.538 degrees
Smaller angle 2 = 2x = 2 * 27.692 ≈ 55.385 degrees
The question states that the sum of the two smaller angles in the triangle is equal to the larger angle in the parallelogram.
Let's assume that the measure of the larger angle in the parallelogram is y. Therefore, the sum of the two smaller angles in the triangle is also y.
We can set up an equation:
41.538 + 55.385 = y
y = 96.923
Therefore, the measure of the smaller angle of the parallelogram is 96.923 degrees.