Question

In quadrilateral ABCD, A is 21 degrees more than 3 times B, C is 2 degrees less than B multiplied by 5, and D is 2 times the size of B. Determine the measure of each interior and each exterior angle of this quadrilateral.

a) A: 84°, B: 21°, C: 99°, D: 42°
b) A: 69°, B: 23°, C: 121°, D: 46°
c) A: 63°, B: 19°, C: 113°, D: 38°
d) A: 75°, B: 25°, C: 125°, D: 50°

Answer 1

To find the angle measures, denote B as x and use given relationships. Solve 3x + 21 + 5x - 2 + 2x + x = 360 to find x, then calculate angles A, C, and D. The exterior angles are the complements of their respective interior angles.

Step-by-step explanation:

To determine the measure of each interior and exterior angle of quadrilateral ABCD, we can use the information given and the fact that the sum of the interior angles of any quadrilateral is 360 degrees. Let's denote the measure of angle B as x.

• Angle A is 21 degrees more than 3 times B, so A = 3x + 21.
• Angle C is 2 degrees less than 5 times B, so C = 5x - 2.
• Angle D is 2 times the size of B, so D = 2x.

Adding these up and setting them equal to 360 gives us the following equation:

3x + 21 + 5x - 2 + 2x + x = 360

Solving for x will give us the measure of angle B, and then we can find A, C, and D by substitution.

The measure of each exterior angle of the quadrilateral is found by subtracting the interior angle from 180 degrees because the sum of an interior and exterior angle at each vertex of a polygon is 180 degrees.