Question

As shown in Figure 2, it is known that PQRS, VWXY and RTU are all straight lines.

a）Find the value of a + b + c + d + e;
b）Find the sum of the interior angles of the polygon QRTXW.​

Answer 1

a. 360°

b. 540°

Explanation:

a The sum of the exterior angles of any n-sided polygon is always 360°. Therefore:

a + b + c + d + e = 360°

b. Sum of interior angles of an n-sided polygon is given as (n - 2) × 180

The polygon, QRTXW is a 5 sided polygon, therefore n = 5.

Plug in the value of 5 into the equation:

Sum of interior angles of QRTXW = (5 - 2) × 180

= 3 × 180

= 540°