10. WHAT is any trapezoid. A straight line
parallel to the bases cuts [WT], [WA), and to
E, G, and F respectively.
H
a) Calculate WE and ET such that WT = 30 and
2FA = 3HF.
b) Calculate HF, FA, WE and ET such that
HA = 8, WT = 12 and GA = 2WG.
Please answer asap
Hint:using Thales theorem

(a) ET = 18 and WE = 12

(b) FA = 16/3

     HF = 8/3

     ET = 8

     WE = 4

Explanation:

WT = 30 ( WE + ET = 30)

WE = 30 - ET

2FA = 3HF

FA = 3/2HF

WE =?, ET = ?

Line WH, EF and TA are parallel to each other.

(a)

ΔWTA and ΔWHA are congruent to each other

Therefore, by congruency

So,

30 - ET/ ET = HF / 3/2HF

30 - ET / ET = 2HF / 3HF

30 - ET / ET  = 2/3

On solving the above equation we get, ET = 18

WE = 30 - ET

WE = 30 - 18 = 12

Therefore, ET = 18 and WE = 12

(b)

HA = 8 ( HF + FA = 8)

HF = 8 - FA

WT = 12 ( WE + ET = 12 )

WE = 12 - ET

GA = 2WG

HF, WA, WE, ET = ?

ΔWHA and ΔGFA are congruent

So,

8 - FA / FA = WG / 2 WG

On solving the above equation we get,

FA = 16/3

HF + FA = 8

HF + 16/3 = 8

HF = 8/3

ΔWTA and ΔWEG are congruent

So,

12 - ET / ET =  WG / 2WG

On solving the above equation, ET = 8

WE = 12 - ET

WE = 12 - 8

WE = 4

Therefore, FA = 16/3

                  HF = 8/3

                  ET = 8

                  WE = 4

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

answer: 2530

hope this