Mathematics: Question Which description describes the solutions to this inequality? 9 52 А all the possible numbers that are smaller than twenty-five B all the possible numbers that are smaller than ten С all the positive numbers that are larger than twenty-five D all the positive numbers that are greater than ten

Question Which description describes the solutions

queenbroookk

27.06.2021

Given:

QRST is an isosceles trapezoid with RS||QT.

To find:

The value of x, angle R and angle T.

Solution:

If a transversal line intersect two parallel lines then the sum of same sides interior angles is 180 degrees.

$m\angle Q+m\angle R=180$

(6x-22)+(8x+34)=180

14x+12=180

14x=180-12

14x=168

Divide both sides by 14.

$x=\dfrac{168}{14}$

x=12

Now,

$m\angle R=(8x+34)^\circ$

$m\angle R=(8(12)+34)^\circ$

$m\angle R=(96+34)^\circ$

$m\angle R=130^\circ$

We know that the base angles of an isosceles triangle are equal.

$m\angle T=m\angle Q=(6x-22)^\circ$

$m\angle T=(6(12)-22)^\circ$

$m\angle T=(72-22)^\circ$

$m\angle T=50^\circ$

Therefore, $x=12,\ m\angle R=130^\circ$ and $m\angle T=50^\circ$ .

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