This question is incomplete. This is because it lacks the diagram of the wooden bookshelf.
Find attached to this answer the diagram the wooden bookshelf.
Answer:
The measure of ∠C =59°
Explanation:
Step 1
From the diagram, we can see that Angle (3x + 16)° and Angle (5x - 54)° are alternate interior angles.
This means
(3x + 16)° = (5x - 54)°
We solve for x by collecting like terms
16° + 54° = 5x° - 3x°
70° = 2x°
x° = 70°/ 2
x = 35°
Step 2
From the diagram, we can see that Angle C and Angle (3x + 16)° are angles on a straight line
The sum of angles on a straight line = 180°
This means: Angle C + Angle (3x + 16)° = 180°
Since x = 35°
We substitute x for 35° in Angle (3x + 16)°
= 3(35) + 16° = 121°
Hence, Angle C + 121° = 180°
Angle C = 180° - 121°
Angle C = 59°
Therefore, the measure of ∠C is 59°