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