The correct answer is: [C]: " m∠H = 91 ° " .
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Explanation:
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Note:
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m∠F + m∠G = 90 ;
{since 2 complementary angles, by definition, add up to 90°.}.
m∠G + m∠H = 180 ;
{since 2 supplementary angles, by definition, add up to 180°.}
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We are asked to find the smallest value of the " m∠H "
(among the given answer choices):
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Note:
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m∠G = 180 − m∠H ;
m∠H = 180 − m∠G ;
m∠F = 90 − m∠G ;
m∠G = 90 − m∠F ;
m∠G = 180 − m∠H ;
m∠H = 180 − m∠G .
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The question is:
"What is the smallest value of " m∠H "; in whole number, among the answer choices given?" ;
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Note: Consider each of the answer choices given:
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Choice: [A]: " m∠H = 1 " ;
{Note, This value is SMALLEST value among ALL the answer choices.}.
If " m∠H = 1" ; then " m∠G = 179 ", since: " m∠G + m∠H = 180".
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 179" ;
then m∠F would have to equal a "negative number" to get:
" m∠F + m∠G = 90 " ;
So, "Choice [A]: " m∠H = 1 " ; is incorrect.
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Choice [B]: " m∠H = 89 " ;
If "m∠H = 89" ; then "m∠G = 91", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 89 = m∠G ;
→ "m∠G = 91" .}.
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 91" ; then "m∠F " would have to equal a "negative number" to get: "m∠F + m∠G = 90" ;
So; "Choice: [B]: "m∠H = 89" ; is incorrect.
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Choice [C]: " m∠H = 91 " ;
If "m∠H = 91" ; then "m∠G = 89", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 91 = m∠G ; → "m∠G = 89" .}.
Then, could "m∠F + m∠G = 90" ?? YES! Because, if "m∠G = 89" ; then
"m∠F" COULD equal "1" ; and in such a case; "m∠F + m∠G = 1 + 89 = 90."
So; Choice: [C]: " m∠H = 91 " ; is a possible correct answer.
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Let us try the last answer choice:
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Choice [D]: " m∠H = 179 " ;
If "m∠H = 179" ; then "m∠G = 1", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 179 = m∠G ; → "m∠G = 1" .}.
Then, would "m∠F + m∠G = 90" ?? Yes! Because, if "m∠G = 1" ; then "m∠F" would equal "89";
{Note: "m∠F + m∠G = 89 + 1 = 90 " .
{Note: "90 − m∠G = m∠F " ; → "90 − 1 = m∠F " ;
→ m∠F = 89° . }.
→ So; "Choice: [D]: " m∠H = 179 " ; is a possible correct answer.
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Note: The question asks:
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"What is the smallest possible measure of "angle H" {" m∠H "} ?
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The 2 (TWO) possible correct answers are:
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Choice [C]: " m∠H "= 91 " ;
and Choice [D]: " m∠H = 179 " .
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The smallest possible " m∠H" is:
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Answer choice: [C]: " m∠H = 91° " .
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Yes 3,000mm is equal to 3m
Answer:
r = 2
Step-by-step explanation:
= 4r-4
square root both sides
r = 4r-4
r = 2r-2
2r-r = 2
r = 2
Applying the angles of intersecting secants theorem, the measures of the arcs are:
m(KL) = 20°; m(MJ) = 80°.
<h3>What is the Angles Intersecting Secants Theorem?</h3>
When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.
Given the following:
m∠MEJ = 1/2(MJ - KL)
30 = 1/2(MJ - KL)
60 = MJ - KL
KL = MJ - 60
m∠MFJ = 1/2(MJ + KL)
50 = 1/2(MJ + MJ - 60)
100 = 2MJ - 60
2MJ = 100 + 60
2MJ = 160
MJ = 160/2
MJ = 80°
KL = MJ - 60 = 80 - 60
KL = 20°
Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:
m(KL) = 20°; m(MJ) = 80°.
Learn more about angles of intersecting secants theorem on:
brainly.com/question/1626547