Explain why is equal to the sum of the measures of the two nonadjacent interior angles. **What is the name of the property?***
1 answer:
Exterior Angle Property
Step-by-step explanation:
Interior Angle :
The angle formed with in the closed boundary of the triangle is called an interior angle.
In the given figure, α , β and γ are interior angles.
Exterior Angles:
The angle formed outside the closed boundary of the triangle is called an exterior angle.
In the given figure, γ' is an exterior angles.
Sum of the measures of the two non-adjacent interior angles is EQUAL to measure of an exterior angle of a triangle.
⇒ α + β = γ'
This property is known as " Exterior Angle Property"
Also, here angles γ and γ' are making a linear pair.
γ + γ' = 180°
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First we need to determine the type of progression in the question.
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.
Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4
Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2
Final answer:
Recursive rule
a₁ = 2
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.
Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4
Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2
Final answer:
Recursive rule
a₁ = 2
For this case we have the following equation:
We must clear the value of the variable "x" as a function of r, s and t:
If we multiply by "r" on both sides of the equation we have:
If we subtract "t" on both sides of the equation we have:
If we divide by "2" on both sides of the equation we have:
Thus, the value of the variable "x" is:
Answer: