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Using the figure to the right, if RSTU is a rhombus, find measure RST.

sammy [17]

Given:

In rhombus RSTU, $m\angle RUV=(10x-23)^\circ$ and $m\angle TUV=(3x+19)^\circ$ .

To find:

The $m\angle RST$ .

Solution:

We know that, diagonals of a rhombus are angle bisector. So,

$m\angle RUV=m\angle TUV$

$(10x-23)^\circ=(3x+19)^\circ$

$10x-23=3x+19$

Isolating variable terms, we get

$10x-3x=23+19$

$7x=42$

Divide both sides by 7.

$x=\dfrac{42}{7}$

$x=6$

Now,

$m\angle RUV=(10x-23)^\circ$

$m\angle RUV=(10(6)-23)^\circ$

$m\angle RUV=(60-23)^\circ$

$m\angle RUV=37^\circ$

And,

$m\angle TUV=(3x+19)^\circ$ .

$m\angle TUV=(3(6)+19)^\circ$

$m\angle TUV=(18+19)^\circ$

$m\angle TUV=37^\circ$

Now,

$m\angle RUT=m\angle RUV+m\angle TUV$

$m\angle RUT=37^\circ+37^\circ$

$m\angle RUT=74^\circ$

We know that opposite angles of a rhombus are equal.

$m\angle RST=m\angle RUT$

$m\angle RST=74^\circ$

Therefore, the measure of angle RST is $74^\circ$ .

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Thirty-seven is less than the difference of seven and ten times a number.

likoan [24]

Answer:

37< 10x-7

Step-by-step explanation:

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Consider polynomial function f(x) = (x+ 1)(x−2)(x−3).

Paladinen [302]

A) f(x) = 0 <=> x = -1 or x = 2 or x = 3;
b) x∈(-oo, -1) => f(x) < 0;
x∈(-1, 2) => f(x) > 0;
x∈(2, 3) => f(x) < 0;
x∈(3, +oo) => f(x) > 0;

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4 years ago

a true-false test has 8 questions.what is the probability of guessing the correct answer to all of the question?

oksian1 [2.3K]

You have a 50/50 chance

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Which expression is equivalent to 96 ?<br> A. 416<br> B. 4v24<br> 0<br> 6/16<br> D.<br> 166

tangare [24]

Answer:

None are equal.

Step-by-step explanation:

None.

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