Mathematics, 29.07.2019 16:00 selene29

Hl suppose abcd is a rhombus such that the angle bisector of ∠abd meets ad at point k. prove that m∠akb = 3m∠abk.

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Answer from: trillred

1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then

m∠ABK=m∠KBD=x°.

Also m∠ABD=m∠ABK+m∠KBD=2x°.

2. The diagonal BD of rhombus ABCD bisects ∠ABC, then

m∠ABD=m∠DBC=2x°.

This gives you that

m∠ABC=4x°.

3. Angles A and B are supplementary, so

m∠A+m∠B=180°,

m∠A=180°-4x°.

4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus

m∠A+m∠ABK+m∠AKB=180°,

m∠AKB=180°-x°-(180°-4x°),

m∠AKB=3x°=3m∠ABK.

Answer from: ashleypere99

Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.

$\angle ABK\cong \angle DBK$ (Definition of angle bisector)

$m\angle ABK=m\angle DBK$ (Definition of concurrency)

Let as assume the measure of angle ABK is x.

$m\angle ABK=x$

$m\angle ABD=m\angle ABK+m\angle DBK$

$m\angle ABD=x+x$

$m\angle ABD=2x$

All sides of a rhombus are same.

Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.

$m\angle ADB=m\angle ABD$

$m\angle ADB=2x$

According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.

Using exterior angle theorem, we get

$m\angle AKB=m\angle ADB+m\angle DBK$

$m\angle AKB=2x+x$

$m\angle AKB=3x$

$m\angle AKB=3(m\angle ABK)$

Hence proved.

Hl suppose abcd is a rhombus such that the angle bisector of ∠abd meets ad at point k. prove that m∠

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7