Finding a Missing Interior Angle Measure in a Convex Polygon ... - Free Printable

To solve this problem, we need to find the value of angle z in the polygon shown.

Step 1: Count the number of sides

Looking at the shape, we can count how many sides (or corners) it has. There are 7 angles labeled — including z — so this is a 7-sided polygon, also called a heptagon.

Step 2: Use the formula for the sum of interior angles

The formula to find the total sum of all interior angles in any polygon is:

> (Number of sides – 2) × 180°

For a heptagon (7 sides):

> (7 – 2) × 180° = 5 × 180° = 900°

So, all 7 angles together add up to 900 degrees.

Step 3: Add up the known angles

We are given six angles:

- 95°
- 170°
- 155°
- 115°
- 125°
- 110°

Let’s add them step by step:

Start with 95 + 170 = 265

265 + 155 = 420

420 + 115 = 535

535 + 125 = 660

660 + 110 = 770

So, the six known angles add up to 770°.

Step 4: Subtract to find z

Total sum of all angles = 900°
Sum of known angles = 770°

So,

> z = 900° – 770° = 130°

✔ Double-check:
95 + 170 + 155 + 115 + 125 + 110 + 130 = ?
Let’s verify:

95 + 170 = 265
265 + 155 = 420
420 + 115 = 535
535 + 125 = 660
660 + 110 = 770
770 + 130 = 900 → Correct!

Final Answer:
130°