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.
[tex]m\angle Q+m\angle R=180[/tex]
[tex](6x-22)+(8x+34)=180[/tex]
[tex]14x+12=180[/tex]
[tex]14x=180-12[/tex]
[tex]14x=168[/tex]
Divide both sides by 14.
[tex]x=\dfrac{168}{14}[/tex]
[tex]x=12[/tex]
Now,
[tex]m\angle R=(8x+34)^\circ[/tex]
[tex]m\angle R=(8(12)+34)^\circ[/tex]
[tex]m\angle R=(96+34)^\circ[/tex]
[tex]m\angle R=130^\circ[/tex]
We know that the base angles of an isosceles triangle are equal.
[tex]m\angle T=m\angle Q=(6x-22)^\circ[/tex]
[tex]m\angle T=(6(12)-22)^\circ[/tex]
[tex]m\angle T=(72-22)^\circ[/tex]
[tex]m\angle T=50^\circ[/tex]
Therefore, [tex]x=12,\ m\angle R=130^\circ[/tex] and [tex]m\angle T=50^\circ[/tex].
