Final answer:
The value of the unknown angle r in a heptagon is 150 degrees, calculated by subtracting the sum of the given angles from the total sum of interior angles of the heptagon.
Step-by-step explanation:
To find the value of the unknown angle r in a heptagon, we need to know the sum of all angles in a heptagon.
A heptagon has seven sides and the sum of its interior angles can be calculated as (n-2) × 180°, where n is the number of sides.
In the case of a heptagon, this amounts to (7-2) × 180° = 5 × 180° = 900°.
To find the value of r, simply subtract the sum of the given angles from the total sum of angles.
Sum of given angles = 135° + 115° + 100° + 150° + 160° + 90° = 750°
Now, subtract this from the total sum of angles:
900° - 750° = 150°
Therefore, the value of the unknown angle r is 150°.