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mel-nik [20]
3 years ago
6

lila draws a 145° angle.Then ahe divides it into three smaller angels.one of the smaller angles measures 65° ,and the other two

are equal in measure. what is the measure of the other two angles?
Mathematics
1 answer:
morpeh [17]3 years ago
3 0
Each angle is 40 degrees because 145 degrees is split into 3 parts and one of them is 65 degrees so you do 145-65=80 the you have two parts left. so you divide 80 by 2 so each degree is 40 degrees
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PLEASE HELP!!! :))
Nina [5.8K]

For a better understanding of the solution given here please find the attached file which has the relevant diagram.

To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.

Please follow the diagram of a complete understanding of the logic and the solution.

As EF is the angle bisector as given in the question, thus we will have:

m\angle DEK=2\times m\angle DE F=2\times 43^{\circ}=86^{\circ}.

Also, from the Theorem we know that KF will be half of DK and thus, KF will be:KF=\frac{1}{2}DK= \frac{1}{2}\times 16=8 centimeters.

Likewise, from the same theorem we have: m\angle EFD=90^{\circ}

4 0
3 years ago
719927 in expanded form
MAVERICK [17]

700,000 + 10,000 + 9,000 + 900 + 20 + 7


6 0
3 years ago
Find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3
LiRa [457]

The slope of the tangent line to the curve at a point <em>(x, y)</em> is d<em>y</em>/d<em>x</em>. By the chain rule, this is equivalent to

d<em>y</em>/d<em>θ</em> × d<em>θ</em>/d<em>x</em> = (d<em>y</em>/d<em>θ</em>) / (d<em>x</em>/d<em>θ</em>)

where <em>y</em> = <em>r(θ)</em> sin(<em>θ</em>) and <em>x</em> = <em>r(θ)</em> cos(<em>θ</em>). Then

d<em>y</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)

d<em>x</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ)</em> sin(<em>θ</em>)

Given <em>r(θ)</em> = cos(3<em>θ</em>), we have

d<em>r</em>/d<em>θ</em> = -3 sin(3<em>θ</em>)

and so

d<em>y</em>/d<em>x</em> = (-3 sin(3<em>θ</em>) sin(<em>θ</em>) + cos(3<em>θ</em>) cos(<em>θ</em>)) / (-3 sin(3<em>θ</em>) cos(<em>θ</em>) - cos(3<em>θ</em>) sin(<em>θ</em>))

When <em>θ</em> = <em>π</em>/3, we end up with a slope of

d<em>y</em>/d<em>x</em> = (-3 sin(<em>π</em>) sin(<em>π</em>/3) + cos(<em>π</em>) cos(<em>π</em>/3)) / (-3 sin(<em>π</em>) cos(<em>π</em>/3) - cos(<em>π</em>) sin(<em>π</em>/3))

d<em>y</em>/d<em>x</em> = -cos(<em>π</em>/3) / sin(<em>π</em>/3)

d<em>y</em>/d<em>x</em> = -cot(<em>π</em>/3) = -1/√3

4 0
2 years ago
Need more points ??? solve this .....only first part for 50 points .....and follow me also!​
leonid [27]

Answer:

see below

Step-by-step explanation:

i.

= √(3 + 4i)

= 2 + i

ii.

= √(-8 + 6i)

= √2(-4 + 3i)

iii.

= √(-40 - 42i)

= √-2(20 + 21i)

iv.

= √i

= √i

v.

= \sqrt{\frac{2 + 3i}{5 - 4i} } +\sqrt{\frac{2-3i}{5+4i} }

= \sqrt{\frac{-2+23i}{41} } +\sqrt{\frac{2-3i}{46} }

7 0
3 years ago
Please help me out with this I will give 50 points.
Helga [31]
The answer is $32
how?: divide .75 from 24, getting 32. to check if it’s correct, multiply.25 and 32 which should get you 8, subtract 8 from 32 and you should get 24 as the end product
4 0
2 years ago
Read 2 more answers
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