The angles of a convex pentagon are proportional to the numbers 2; 3; 3; 3; 4. find the degree measure

| April 14, 2021 | education

The angles of a convex pentagon are proportional to the numbers 2; 3; 3; 3; 4. find the degree measure of the greater angle of the given pentagon.

Let the coefficient of proportionality of the angles of a given pentagon be x, then the degree measures of the angles will be 2x, 3x, 3x, 3x and 4x (according to the problem statement).

The sum of the angles of a convex polygon is found by the formula 180 ° * (n – 2).

Since n = 5, then 180 ° * (5 -2) = 180 ° * 3 = 540 °.

Let’s compose and solve the equation: 2x + 3x + 3x + 3x + 4x = 540 °.

Whence 15x = 540 °, x = 540 ° / 15 = 36 °.

Hence,

1 angle = 2 * 36 ° = 72 °,

2 angle = 3 angle = 4 angle = 3 * 36 ° = 108 °,

5 angle = 4 * 36 ° = 144 °.

Answer: The degree measure of the larger angle of the pentagon is 144 °.



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