Question

A quadrilateral has two angles that measure 10° and 70°. The other two angles are in a ratio of 3:11. What are the measures of those two angles?

Answer 1

The measures of the unknown angles in the quadrilateral are 60 degrees and 220 degrees.

Step-by-step explanation:

Let's denote the measures of the unknown angles as 3x and 11x, based on the given ratio.

We know that the sum of all angles of a quadrilateral is 360 degrees, so by subtracting the two given angles from the total, we can find the sum of the unknown angles: 360 - 10 - 70 = 280 degrees.

Now, we can set up an equation: 3x + 11x = 280. Solving this equation, we get 14x = 280, which leads to x = 20.

Substituting x back into the equation, we find that the measures of the two unknown angles are 3x = 3(20) = 60 degrees and 11x = 11(20) = 220 degrees.

Answer 2

The measures of those two angles are 60° and 220°

Step-by-step explanation:

• The sum of the measures of the angles of any quadrilateral is 360°

Let us solve the question

∵ A quadrilateral has two angles that measure 10° and 70°

→ By using the rule above, subtract their measure from 360

∴ The sum of the other two angles = 360° - 10° - 70°

∴ The sum of the other two angles = 280°

∵ The other two angles are in a ratio of 3: 11

→ Find the sum of the parts of the ratio

∵ The sum of the parts of the ratio = 3 + 11 = 14

∵ The sum of the measures of these 2 angles is 280°

→ By using the ratio method

→ m∠1 : m∠2 : their sum

→ 3 : 11 : 14

→ x : y : 280°

→ By using cross multiplication

∵ x × 14 = 3 × 280

∴ 14x = 840

→ Divide both sides by 14

∴ x = 60

∴ m∠1 = 60°

∵ y x 14 = 11 x 280

∴ 14y = 3080

→ Divide both sides by 14

∴ y = 220

∴ m∠2 = 220°

∴ The measures of those two angles are 60° and 220°