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

I need the answers for B. C. and F. please show the work-example-1
User Angrykoala
by
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1 Answer

8 votes
8 votes

Answer:

Δᶜ; q = 36°

Δᵈ; m = 42.5°

Δ; y = 60°

Δᶠ; t = 26.5°

Explanation:

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

Given the triangle labelled 'c.', we'll call it Δ, 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 Δ, 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 Δ, we deduce:

180° = Sum of interior angles

180° = 90° + 2t + ( t + 10.5° )

90° = 3t + 10.5°

3t = 79.5°

t = 26.5°

User Tomas Kulhanek
by
2.9k points