Question

Assume we cut the last piece of the pie into two sections (1 and 2) along ray BD

such that m∠ABD = 2x+3, m∠CBD = 4x+7, and m∠ABC = 40°. Based on this information,

would you ask for section 1 or section 2 (you have to pick one) for dessert? Provide numerical

evidence to back up your choice. Explain your reasoning and your methods.

Answer 1

Section 2

Explanation:

I will pick the section with the largest angle.

Let's determine the size of the angle of each section.

Given:

m∠ABD = 2x+3,

m∠CBD = 4x+7,

m∠ABC = 40°

Thus:

m<ABD + m<CBD = m<ABC (angle addition postulate)

Substitute

2x + 3 + 4x + 7 = 40

Add like terms

6x + 10 = 40

6x + 10 - 10 = 40 - 10

6x = 30

6x/6 = 30/6

x = 5

✔️m∠ABD = 2x+3

Plug in the value of x

m<ABD = 2(5) + 3 = 13° (section 1)

✔️m∠CBD = 4x+7

m∠CBD = 4(5) + 7

m∠CBD = 27° (section 2)

✅I will pick section 2 because it is the section with the largest angle, which means it is the biggest.