The interior angles of a quadrilateral are in the ratio 2:3:4:6. What is the degree measur… — ACT

The interior angles of a quadrilateral are in the ratio $2:3:4:6$ . What is the degree measure of the largest interior angle of the quadrilateral?

144

The sum of the interior angles of a quadrilateral is

360^\circ

. Given the ratio

2:3:4:6

, the sum of the parts is

2 + 3 + 4 + 6 = 15

. The value of one part is

360^\circ \div 15 = 24^\circ

. The largest angle corresponds to the largest part of the ratio, which is

6

. Therefore, the largest angle measure is

6 \times 24^\circ = 144^\circ

Determine the sum of the interior angles of a quadrilateral.

The sum of the interior angles of any quadrilateral is

360^\circ

This is a fundamental property of quadrilaterals, which can also be derived using the formula

(n - 2) \times 180^\circ

with

n = 4

Calculate the total number of parts in the given ratio.

The sum of the ratio parts is

2 + 3 + 4 + 6 = 15

Adding the parts of the ratio allows us to find the size of a single share of the total angle sum.

Find the measure of one part of the ratio.

One part is equal to

360^\circ \div 15 = 24^\circ

Dividing the total sum of the angles by the sum of the ratio parts determines the angle measure per ratio unit.

Multiply the largest ratio part by the value of one part to find the largest angle.

The largest angle is

6 \times 24^\circ = 144^\circ

The largest interior angle corresponds to the largest number in the ratio, which is

6

Using ratios to find angle measures in a polygon.

Tahmini Süre:45s

Soru