Question

The angles of a quadrilateral are (x - 10)°, x, (x + 10)°, (x + 20)°. Find each angle.

• A. 70°, 80°, 90°, 100°
• B. 75°, 85°, 95°, 105°
• C. 80°, 90°, 100°, 110°
• D. 85°, 95°, 105°, 115°

Answer 1

The correct option is B 75°, 85°, 95°, 105°

The sum of the angles of the quadrilateral is 360°.

Given the angles, (x - 10)°, x, (x + 10)°, (x + 20)°.
Then, (x - 10)°+ x+ (x + 10)°+ (x + 20)° = 360°.

$\to$ x - 10° + x + x + 10° + x + 20° = 360°.
$\to$ 4x -10° + 10° + 20° = 360°.
$\to$ 4x + 20° = 360°.
$\to$ 4x = 360° - 20° = 340°.
$\to$ x = $\frac{340°}{4}$ = 85°.
$\to$ x = 85°

Then the angles are

• (x - 10)° = (85 - 10)° = 75°
• x = 85°
• (x + 10)° = (85 + 10)° = 95°
• (x + 20)° = (85 + 20)° = 105°

So the required angles are 75°, 85°, 95° 105°.