Consider the non-right triangle below. Suppose that m∠BCA=71∘, and that x=31 cm and y=50 cm. What is the degree measure of ∠ABC?
m∠ABC=
​

m<ABC = 71°

Step-by-step explanation:

Given:

m<BCA = 71°

x = 31 cm

y = 50 cm

Required:

m<ABC

Solution:

First, find AB, using Cosine Rule:

AB² = x² + y² - 2xy*Cos m<ABC

Plug in the values

AB² = 31² + 50² - 2(31)(50)*cos 71

AB² = 3,461 - 1,009.26128

AB² = 2,451.73872

AB = √2,451.73872

AB = 49.5150353 ≈ 50 cm

✔️Since AB ≈ 50 cm, and AC is also 50 cm, it means the triangle is an isosceles triangle.

Therefore, the base angles of ∆ABC, <ABC and <BCA, would be congruent.

Therefore,

m<BCA = m<ABC = 71°

m<ABC = 71°

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x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)