sum of the 5th and 10th terms of an arithmetic sequence which are equal to the 20th term (80). find the 30th term
1 answer:
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Answer:
The true statements are:
m∠ 3 + m∠ 4 = 180° ⇒ 1st
m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd
m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd
Step-by-step explanation:
* Look to the attached diagram to answer the question
# m∠ 3 + m∠ 4 = 180°
∵ ∠ 3 and ∠ 4 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠ 3 + m∠ 4 = 180° ⇒ <em>true</em>
# m∠ 2 + m∠ 4 + m∠ 6 = 180°
∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle
∵ The sum of the measures of interior angles of any Δ is 180°
∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ <em>true</em>
# m∠ 2 + m∠ 4 = m∠ 5
∵ In any Δ, the measure of the exterior angle at one vertex of the
triangle equals the sum of the measures of the opposite interior
angles of this vertex
∵ ∠ 5 is the exterior angle of the vertex of ∠ 6
∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6
∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ <em>true </em>
# m∠1 + m∠2 = 90°
∵ ∠ 1 and ∠ 2 formed a straight angle
∵ The measure of the straight angle is 180°
∴ m∠1 + m∠2 = 90° ⇒ <em>Not true</em>
# m∠4 + m∠6 = m∠2
∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle
∵ There is no given about their measures
∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is
equal to the measure of ∠ 2
∴ m∠4 + m∠6 = m∠2 ⇒ <em>Not true</em>
<em></em>
# m∠2 + m∠6 = m∠5
∵ ∠ 5 is the exterior angle at the vertex of ∠ 6
∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ <em>Not true</em>
Answer:
Part 1) The perimeter is
Part 2) The area is
Step-by-step explanation:
Part 1) Find the perimeter
we know that
The perimeter is equal to the circumference of the exterior circle plus the circumference of the interior circle
so
Part 2) Find the area
we know that
The area of the figure is equal to the area of the larger circle minus the area of the smaller circle
so