Pentagon Angles: Finding the Missing Angle

To determine the measure of the fifth angle in a pentagon, we utilize the property concerning the sum of its interior angles.

Sum of Interior Angles Formula

The total sum of the interior angles for any polygon can be calculated using the formula:

Sum = $(n-2) \times 180^\circ$

where $n$ represents the number of sides of the polygon.

Calculating for a Pentagon

A pentagon has 5 sides, so $n=5$. Plugging this into the formula gives the sum of its interior angles:

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

Given Angles and Sum Calculation

The problem provides four angles of the pentagon:

• $70^\circ$
• $110^\circ$
• $135^\circ$
• $95^\circ$

Let the unknown fifth angle be represented by $x$. The sum of the four known angles is:

$70^\circ + 110^\circ + 135^\circ + 95^\circ = 410^\circ$

Determining the Fifth Angle

The sum of all five interior angles must equal $540^\circ$. Therefore, we can write the equation:

$410^\circ + x = 540^\circ$

To find the value of $x$, we isolate it:

$x = 540^\circ - 410^\circ$

$x = 130^\circ$

Thus, the measure of the fifth angle of the pentagon is $130^\circ$.