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Answered

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Can you help me, please?​

Can You Help Me Please class=

Sagot :

Answer:

a. 18

b.144

c.108

Step-by-step explanation:

Using the given, Angle R equal 5x-54 and Angle T is 8u.

Also RS is congruent to ST. Since SR is congruent to ST, their opposite angles are also congruent using base angle theorem. So angle R is equal to Angle T. However, STU is a exterior angle so STU isn't congruent to SRT.

However, we can add , interior angle T, and STU to 180 to find x.

Interior angle T=SRT so interior angle t=5x-54.

Set up equation

[tex]5x - 54 + 8x = 180[/tex]

[tex]13x - 54 = 180[/tex]

[tex]13x = 234[/tex]

[tex]x = 18[/tex]

b.Plug 18 into 8x

[tex]8(18) = 144[/tex]

STU=144

c. Using the triangle exterior angle theorem, the exterior angle is equal to the measure of the sum of two non adjacent angles.

Angle S and Angle R are the non adjacent angle to STU.

So we cast up this equation.

[tex]5x - 54 + s = 180[/tex]

plug 18 in for x

[tex]5(18) - 54 + s = 144[/tex]

[tex]90 - 54 + s = 144[/tex]

[tex]36 + s = 144[/tex]

s=108

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