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MrRoyalidn

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]

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