Question

the angles of a Pentagon are in a ratio of 2 : 3 : 4 : 5: 6 . find the measurement of the largest angle​

Answer 1

Answer:

135degree

Step-by-step explanation:

Let the angles of the Pentagon be 2x,3x,4x,5x, and 6x

Let n be the number of sides.

In a regular Pentagon, sum of interior angles=(n−2)×180 ∘

=(5−2)×180 ∘

=540 ∘

According to the question,

2x+3x+4x+5x+6x=540 ∘

⇒20x=540 ∘

⇒x=

20

540 ∘

=27 ∘

The interior angles of the given pentagon

2x=2×27 ∘

=54 ∘

3x=3×27 ∘

=81 ∘

4x=4×27 ∘

=108 ∘

5x=5×27 ∘

=135 ∘

6x=6×27 ∘

=162 ∘

thus, the interior angles of the Pentagon are 54 ∘ ,81 108∘ ,135 ∘ and 162 ∘

Sum of first and second angle=54 ∘ +81 ∘

=135 ∘