Question

Please help, explain the best you can!

Answer 1

∠BAD = 109°

∠DAC = 111°

Explanation:

We need to approach this question with the knowledge that these three angles added together will equal 360°.

Once we recognize that, we can set up an equation.

140 + (2x + 4) + (2x + 6) = 360

From here, we can do some simplification.

4x + 150 = 360

Now, we just solve for x.

4x = 210

x = 52.5

Now that we have an x value, just plug it in to the equations for the angles in your photo, and you will get the angle measurement!

For example, ∠BAD = 2(52.5) + 4 = 109°

Do the same for ∠DAC!

Answer 2

∠BAD = 109°

∠DAC = 111°

Explanation:

This is essentially a triangle, correct? Something to know is that these angles in a triangle add up to 360°.

In mathematical terms, this would look like: 140 + (2x + 4) + (2x + 6) = 360

Now, we solve for x.

140 + (2x + 4) + (2x + 6) = 360 (Subtract 140 from both sides to get x's on one side)

2x + 4 + 2x + 6 = 220 (Add like terms: 2x + 2x and 4 + 6)

4x + 10 = 220 (Subtract 10 from both sides to get x on one side)

4x = 210 (Divide both sides by 4 to get x by itself)

x = 52.5

Now that we know what x equals, we can plug it in to find ∠BAD and ∠DAC.

2x + 4 → 2(52.5) + 4 = 109

2x + 6 → 2(52.5) + 6 = 111