425,654 views
22 votes
22 votes
The angle measurements in the diagram are represented by the following expressions

The angle measurements in the diagram are represented by the following expressions-example-1
User Nabrond
by
2.9k points

1 Answer

15 votes
15 votes

Answer:

∠A is equal to 73°

Explanation:

Because the two lines that move roughly bottom/left to top/right are marked as being parallel, we can say that ∠A + ∠B = 180°

With that we can take the two equations at the top, and add them together for a sum of 180°:

6x - 35° + 3x + 53° = 180°

9x + 18° = 180°

x + 2° = 20°

x = 18°

Now that we have x, we can solve for ∠A:

∠A = 6x - 35°

∠A = 6(18°) - 35°

∠A = 108° - 35°

∠A = 73°

We can test our answer by solving for ∠B. We know that ∠A and ∠B add up to 180°, so ∠B = 180° - ∠A = (180 - 73)° = 107°. Now let's solve for be given x and the original equation, and see if we have the right numbers:

∠B = 3x + 53°

∠B = 3(18°) + 53°

∠B = 54° + 53°

∠B = 107°

Which matches up, showing us that we have the correct answer.

User Uli Sotschok
by
2.8k points