Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Given
[tex]\angle S = 45[/tex]
[tex]\angle U = 4x - 1[/tex] --- (not clear but that is what I'm able to read)
[tex]\angle Q = 100[/tex]
Required
Find x
From the attachment, the corresponding angles of both triangles are equal:
This implies that:
[tex]\angle P = \angle S = 45[/tex]
[tex]\angle U = \angle R = 4x - 1[/tex]
[tex]\angle Q = \angle T = 100[/tex]
Apply angle sums property
[tex]\angle S +\angle T +\angle U =180[/tex]
This becomes
[tex]45 + 4x - 1 +100 = 180[/tex]
Collect like terms
[tex]4x= 180-45-100+1[/tex]
[tex]4x= 36[/tex]
[tex]x = 9[/tex]
