Question

In parallelogram ABCD, angle A is 3x, and angle B is 2x+60. Find the measure of all angles

Answer 1

By utilizing the properties of parallelograms, x is found to be 24. This leads to angle A and angle C each being 72 degrees, and angle B and angle D each being 108 degrees.

Step-by-step explanation:

To find the measure of all angles in parallelogram ABCD where angle A is 3x and angle B is 2x+60, we can use the properties of parallelograms. In a parallelogram, opposite angles are equal, and the sum of consecutive angles is 180 degrees.

Since angle A is 3x, angle C, being the opposite angle, is also 3x. Likewise, angle B is 2x + 60, so angle D (opposite angle) is also 2x + 60. To find x, we use the fact that angle A plus angle B equals 180 degrees:

1. 3x + (2x + 60) = 180
2. 5x + 60 = 180
3. 5x = 120
4. x = 24

With x = 24, we can calculate each angle:

• Angle A: 3x = 3(24) = 72 degrees
• Angle B: 2x + 60 = 2(24) + 60 = 108 degrees
• Angle C: 3x = 72 degrees (same as angle A)
• Angle D: 2x + 60 = 108 degrees (same as angle B)