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3 years ago

If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing measure.

Mathematics

1 answer:

sleet_krkn [62]3 years ago

4 0

Answer:

∠1=∠9=43°, ∠2=∠7= 17°, ∠4=∠5=∠6=60°, ∠3=∠8=120°

Step-by-step explanation:

Given ABC is an isosceles triangle and DBE is an equilateral triangle. we have to find each missing measure.

In triangle ABC,

∠1=∠9 (∵isosceles triangle)

⇒ 4x+3=9x-47

⇒ 9x-4x=3+47 ⇒ 5x=50 ⇒ x=10

Hence, ∠9=∠1=(4x+3)°=4(10)+3=43°

Also, given ΔBDE is an equilateral triangle, and all angle of equilateral triangle are equal.

∴ ∠4+∠5+∠6=180°

⇒ ∠4+∠4+∠4=180° ⇒ 3∠4 = 180° ⇒ ∠4 = 60°

∴ ∠4=∠5=∠6=60°

By exterior angle property, ∠3=∠5+∠6=60°+60°=120°

∠8=∠5+∠4=60°+60°=120°

In ΔABD, ∠1+∠2+∠3=180°

⇒ 43°+120°+∠2=180°⇒ ∠2 = 17°

In ΔABD, ∠9+∠8+∠7=180°

⇒ 43°+120°+∠7=180°⇒ ∠7= 17°

Step-by-step explanation:

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Observe attached image

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If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing measure.​

If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing measure.