Question

I need the answers for B. C. and F. please show the work

Answer 1

Answer:

Δᶜ; q = 36°

Δᵈ; m = 42.5°

Δᵉ; y = 60°

Δᶠ; t = 26.5°

Step-by-step explanation:

The sum of interior angles of a triangle is 180°, always!

Given the triangle labelled 'c.', we'll call it Δᶜ, we can form an equation:

180° = Sum of interior angles

180° = 3q + q + q

180° = 5q

q = 36°

Given triangle labelled 'd.', we'll call it Δᵈ, we deduce:

180° = Sum of interior angles

180° = m + 2m + ( m + 10° )

180° = 4m + 10°

4m = 170°

m = 42.5°

Given the triangle labelled 'e', we'll call it Δᵉ, we deduce:

180° = Sum of interior angles

180° = 90° + y + ( y - 30° )

180° = 90° + 2y - 30°

180° = 60° + 2y

120° = 2y

y = 60°

"...We use the same equation because the rule of the sum of interior angles is mathematically universal and applies to all triangles..."

Given the last triangle, let's call it Δᶠ, we deduce:

180° = Sum of interior angles

180° = 90° + 2t + ( t + 10.5° )

90° = 3t + 10.5°

3t = 79.5°

t = 26.5°