Question

the angles of a quadrilateral have measures of 5x, 3x+20, 4x+5, and 5x-5. The measure of one of the angles is

Answer 1

Question:

The angles of an quadrilateral have measures of 5x, 3x+20, 4x+5 and 5x-5. Find the measure if each of the angle.

Answer:

The angles are 100°, 80°, 85° and 95° respectively.

Step-by-Step Process:

All angles of the quadrilateral add up to 360°.

Therefore,

$5x \: + (3x \: + 20) + (4x + 5) + (5x + 5) = 360 \\ (5x + 3x + 4x + 5x) + (20 + 5 - 5) = 360 \\ 17x + 20 = 360 \\ 17x = 360 - 20 \\ 17x = 340 \\ x = \frac{340}{17} \\ x = 20$

Now, putting the values into places:

Angle 1 = 5x = 5 × 20

= 100°

Angle 2 = 3x + 20 = 3 × 20 + 20

= 60 + 20

= 80°

Angle 3 = 4x + 5 = 4 × 20 + 5

= 80 + 5

= 85°

Angle 4 = 5x - 5 = 5 × 20 - 5

= 100 - 5

= 95°