what is the value of angle x?

[sunaina jain]

Please let me know how to solve this.

What is the value of angle x (angle QSU)?
Given: If length QR = RS and lenght of ST = TU. Also angle QPU = 90 degree.

[sunnyjohn]

See this:

[adpatel87]

I thought the previous explanation posted was quite confusing so I tried the question out myself:

LET:
L= Angels RSQ & RQS (equal sides of a triangle)
M= Angels TSU & SUT (equal sides of a triangle)
R= Angel PRT
T= Angel RTP
X= Angel QSU

So looking at line RT we have:
L + X + M = 180
Looking at triangle RPT we have:
90 + T + R = 180
Looking at triangle SUT we have:
2M + T = 180
Looking at triangle RQS we have:
2L + R = 180

All together:
1. L + X + M = 180
2. 90 + T + R = 180
3. 2M + T = 180
4. 2L + R = 180

Simplify 2:
T + R = 90

Combine 3 & 4 to get:
2M + 2L + T + R = 360
2M + 2L = 360 - 90 (substitute 2)
2M + 2L = 270
M + L = 135

now taking this equation and substituting it in 1gives:

X + 135 = 180
X = 45