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Lemur [1.5K]
3 years ago
13

What is the measure of angle q°? 150° 540° 95° 100°

Mathematics
1 answer:
seraphim [82]3 years ago
8 0
150.

All the angles in a pentagon sum to 540
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The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of
Brrunno [24]

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The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

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Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

<em>By using cosine rule</em>

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

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∴ s2 = 2r√3

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∴ The side of the outer Δ is double the side of the inner Δ

<em>By using similarity ratio</em>

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

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dolphi86 [110]

720 \div 6 = 120
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