Testinar Grade 8 math

Interior Angles of Polygons

Learn to reason about and solve Grade 8 problems involving Interior Angles of Polygons.

CH05-13 Geometry and Measurement

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

The figure shows a pentagon with interior angles. If \(\angle A = 100°\), \(\angle B = 120°\), \(\angle C = 110°\), and \(\angle D = 130°\), what is \(\angle E\)?
1. 80°
2. 100°
3. 120°
4. 140°
A regular hexagon is shown with one interior angle marked. What is the measure of the marked interior angle?
1. 100°
2. 110°
3. 120°
4. 130°
A hexagon has interior angles: \(85°, x, 125°, 140°, 110°, 98°\). Find \(x\).
1. 162°
2. 227°
3. 232°
4. 237°
A hexagon has five known interior angles: \(120°, 100°, 90°, 115°, 130°\). What is the sixth angle?
1. 145°
2. 155°
3. 165°
4. 175°
A quadrilateral has angles \(A = 85°\), \(B = 95°\), \(C = 100°\). What is angle \(D\)?
1. 70°
2. 80°
3. 90°
4. 100°
A hexagon has five interior angles: \(88°, 112°, 95°, 118°, 147°\). Find the sixth angle.
1. 150°
2. 160°
3. 170°
4. 180°
A heptagon has six interior angles: \(130°, 125°, 140°, 135°, 128°, 132°\). Find the seventh angle.
1. 100°
2. 105°
3. 110°
4. 115°
A nonagon (9-sided polygon) has eight interior angles: \(140°, 142°, 138°, 140°, 136°, 141°, 139°, 137°\). Find the ninth angle.
1. 145°
2. 147°
3. 150°
4. 152°

Teacher and parent reference

Answer key and explanations

A. 80°
The sum of angles in a pentagon is 540°. So \(\angle E = 540 - 100 - 120 - 110 - 130 = 80°\).
C. 120°
Each interior angle of a regular hexagon is \(\frac{(6-2)\times180}{6}=\frac{720}{6}=120°\).
A. 162°
The sum of interior angles in a hexagon is 720°. The known angles add to \(85+125+140+110+98=558°\), so \(x=720-558=162°\).
C. 165°
A hexagon's interior angles add to 720°. The known angles add to \(120+100+90+115+130=555°\), so the missing angle is \(720-555=165°\).
B. 80°
The sum of interior angles in a quadrilateral is 360°. So \(D = 360 - 85 - 95 - 100 = 80°\).
B. 160°
A hexagon's interior angles add to 720°. The known angles add to \(88+112+95+118+147=560°\), so the sixth angle is \(720-560=160°\).
C. 110°
A heptagon's interior angles add to \((7-2)\times180=900°\). The known angles add to \(130+125+140+135+128+132=790°\), so the seventh angle is \(900-790=110°\).
B. 147°
A nonagon's interior angles sum to \((9-2)\times180=1260°\). The eight known angles sum to \(140+142+138+140+136+141+139+137=1113°\), so the ninth angle is \(1260-1113=147°\).