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lana66690 [7]
4 years ago
6

13 + 2k = 3k + 4(k - 3)​

Mathematics
1 answer:
Trava [24]4 years ago
8 0

Answer:

k=5

Step-by-step explanation:

7

k

−

12

=

13

+

2

k

Move all terms containing

k

to the left side of the equation.

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If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing measure.​
sleet_krkn [62]

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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