I need help! can anybody help?

Mathematics

1 answer:

Alexandra [31]2 years ago

5 0

Answer:

i, m, and then k (use my method to do the other one)

Step-by-step explanation:

The longer than angle the longer the side tht is opposite to it... so for example, each angle and its opposite correspond to each other.. so K it is side K and so on...

first u should find the missing angles, for A, we know the angles 118 and 28 and a triangle is a total of 180 degrees, so add 118 and 28, which will give u 146, now subtract tht from 180 and u get 34, so the missing angle M is 34, now we can see which angles correspond to which side:

K = k

M = m

L = l

so the shortest will be l, then it will be m, and then it will be k

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$