1 Answer

Jeremy McNees · Answer 1 · 2022-09-28T20:32:02+0000

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=(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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