The interior angles of a convex pentagon are given as (2x + 10)^\circ, (x + 25)^\circ, (3x… — JAMB UTME

The interior angles of a convex pentagon are given as $(2x + 10)^\circ$ , $(x + 25)^\circ$ , $(3x - 15)^\circ$ , $(2x + 30)^\circ$ , and $(2x + 10)^\circ$ . What is the value of $x$ ?

A
30
48Answer
C
60
D
66

Answer

The value of

x

is 48.

For a pentagon (

n = 5

), the sum of interior angles is

(5 - 2) \times 180^\circ = 540^\circ

. Summing the five given interior angle expressions yields

10x + 60

. Equating

10x + 60 = 540

gives

10x = 480

, which solves to

x = 48

Step-by-Step Solution

Calculate the sum of interior angles of a 5-sided polygon (pentagon)

Sum

= (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ

The formula for the sum of interior angles of a polygon with

n

sides is

(n - 2) \times 180^\circ

Sum the given algebraic expressions for the interior angles

(2x + 10) + (x + 25) + (3x - 15) + (2x + 30) + (2x + 10) = 10x + 60

Combine like terms for the

x

terms and constant terms.

Equate the sum of expressions to

540^\circ

and solve for

x

10x + 60 = 540 \implies 10x = 480 \implies x = 48

Subtract 60 from both sides and divide by 10 to isolate

x

Key Concept

Interior Angle Sum of Polygons

Estimated Time:1m 15s

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