![billy12008](/avatars/46578.jpg)
billy12008
03.02.2020 •
Mathematics
Ireally dont understand will give 100 points
show !
circle with tangent mn.
msn = 60°; mqs = x; mqp = x + 40; m pn = 2x-16
find x =
angle 5 =
angle 1 =
angle 2 =
angle 6 =
angle 7 =
angle 3 =
angle 8 =
angle 4 =
mpn =
Solved
Show answers
More tips
- H Health and Medicine How does childbirth happen: everything future mothers need to know...
- H Health and Medicine What Are the Best Vitamins? A Scientific View on Vitamin Supplements...
- A Auto and Moto How to Deregister a Car in Moscow?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- A Auto and Moto How to choose the right drive for your BMW...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- L Leisure and Entertainment Mysteries of the Name Vyacheslav Dobrynin...
- H Health and Medicine What makes Graves’ disease dangerous?...
- F Food and Cooking When is Easter in 2011?...
- C Computers and Internet Best Antivirus: How to Choose Protection for Your Computer?...
Answers on questions: Mathematics
- M Mathematics People who get angry easily tend to have more heart disease. That is the conclusion of a study that followed a random sample of 12,986 adults for about four years. All subjects...
- M Mathematics (02.03 MC) triangle ADB, point C lies on segment AB and forms segment CD, angle ACD measures 90 degrees. Point A is labeled jungle gym and point B is labeled monkey bars. Beth is...
- M Mathematics Here is a rectangle abcd. the length of the rectangle is ... Here is a rectangle abcd. the length of the rectangle is increased by 10%. the width of the rectangle is increased by...
- M Mathematics Which statement is true regarding the functions on the graph...
- M Mathematics Consider the diagram.What is the length of segment AB? 7 9 18 25...
- M Mathematics 1 Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Match each equation with its y-intercept.(0,5)AIO(0,8(0,8)(0,5)Equationsy-interceptscat by16x...
- M Mathematics Brain Builders Processes 12. & Practices 5 Use Math Tools Luisa is helping to tile a hallway. How many square tiles will be needed to fill the area? Complete the diagram to...
- M Mathematics Which point best represents 55. Explain your answer. A B C 5 6 7 9 10 11...
- M Mathematics Answer please mmmmmmmmmmmmmmmmmmmmmmmmmmmmm...
- M Mathematics Can I please have help? A group of hikers buy 8 bags of trail mix. Each bag of Trail Mix contains 3 1/2 cups of Trail Mix. The trail mix is shared evenly among 12 hikers. How many...
Ответ:
Part 1) The value of x is 69°
Part 2) Angle 1=64.5°
Part 3) Angle 2=84.5°
Part 4) Angle 3=31°
Part 5) Angle 4=84.5°
Part 6) Angle 5=95.5°
Part 7) Angle 6=95.5°
Part 8) Angle 7=54.5°
Part 9) Angle 8=30°
Step-by-step explanation:
Part 1) Find the value of x
we know that
arc SN+arc QS+arc QP+arc PN=360° > by complete circle
substitute the values
60°+x°+(x+40)°+(2x-16)°=360°
solve for x
84°+4x°=360°
4x=276°
x=69°
Part 2) Find the measure of angle 1
we know that
The inscribed angle is half that of the arc it comprises
so
m∠1=(1/2)[arc QSN]
arc QSN=arc QS+SN
arc QSN=x+60°=69°+60°=129°
substitute
m∠1=(1/2)[129°]=64.5°
Part 3) Find the measure of angle 2
we know that
The measure of the inner angle is the semi-sum of the arcs that comprise it and its opposite
m∠2=(1/2)[arc SN+arc QP]
substitute the values
m∠2=(1/2)[60°+(x+40)°]
m∠2=(1/2)[60°+(69+40)°]
m∠2=(1/2)[169°]=84.5°
Part 4) Find the measure of angle 3
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
m∠3=(1/2)[arc PN-arc SN]
substitute the values
m∠3=(1/2)[(2x-16)°-60°]
m∠3=(1/2)[(2(69)-16)°-60°]
m∠3=(1/2)[62°]=31°
Part 5) Find the measure of angle 4
we know that
m∠4=m∠2 > by vertical angles
so
m∠4=84.5°
Part 6) Find the measure of angle 5
we know that
m∠5+m∠2=180° > by supplementary angles
so
m∠5+84.5°=180°
m∠5=180°-84.5°=95.5°
Part 7) Find the measure of angle 6
we know that
m∠6=m∠5 > by vertical angles
so
m∠6=95.5°
Part 8) Find the measure of angle 7
we know that
The inscribed angle is half that of the arc it comprises
so
m∠7=(1/2)[arc QP]
arc QP=(x+40)°=(69+40)°=109°
substitute
m∠7=(1/2)[109°]=54.5°
Part 9) Find the measure of angle 8
we know that
The inscribed angle is half that of the arc it comprises
so
m∠8=(1/2)[arc SN]
arc SN=60°
substitute
m∠8=(1/2)[60°]=30°
Ответ:
Shania is correct.
Step-by-step explanation:
For a right angled triangle, given two sides and an angle, we can use the sine rule or the various trigonometry identities to solve the triangle;
a/sin A = b/sinB
and
sin (angle) = opposite side/hypotenuse
cos (angle) = adjacent side/hypotenuse
tan (angle) = opposite/ adjacent
assuming a is the opposite side of angle A and b is also opposite of angle B
Otherwise, the only way to solve a triangle given two sides only is by the use of the Pythagoras theorem.
Hence, Shania is correct.