Question

A carpenter is making a wooden bookshelf. The image below shows the design of the bookshelf which is not to scale. Board 1 is parallel to Board 2. Enter the measure of ∠C.

Answer 1

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°

Step-by-step 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°