Member • Nov 2, 2011

## Solution to Grand Quiz Question #2

**figure**we have,

[1] PR = QR

[2] QS = SR

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In

**Figure 2**, parallel to PQ, we draw SU

Because [1] and PQ || SU, we get

[3] RS =RU

[4] PS = QU

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In

**Figure 3**, we draw line PU.

From [4], and PQ = QP, and angle RPQ = RQP (=80),

the triangle PQS equals to triangle PQU.

So

[5] PU = QS

From [2], PU = SR

From [3], we get

[6] PU = RU

So angle RPU = 20, TPU = 10, UPQ = 60,

[7] SVU = 60

[8] PQ = QV = VP

From [5], [7] and [8], we get

[9] SU = UV = VS

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In

**Figure 4**, we draw UW vertical to PR.

From [6] and angle RPU = PRU, we get triangle PUW equals to triangle RUW. So

[10] PW = RW

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**Figure 5**

In Figure 5, we draw RX.

From [10] and UW vertical to PR, we get

[11] angle SRX = SPX = 10

[12] RX = PX

From [11], we get

[13] angle URX = 10 = SRX

[13'] angle URX = UPX