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In triangle QRS, if QR is congruent to RS, angle Q = 8x - 17, angle R = 19x + 4, & angle S = 5x + 1, find x & the measure of each angle.

Respuesta :

Blacklash

Answer:

        Angle Q = 31°

        Angle R = 118°

        Angle S = 31°

Explanation:

  If QR is congruent to RS, from figure given we have angle Q = angle S.

  Angle Q = 8x -17

  Angle R = 19x + 4

  Angle S = 5x + 1

We have,

        8x -17 = 5x + 1

         3x = 18

          x = 6

So,

        Angle Q = 8*6 -17 = 31°

        Angle R = 19*6 + 4 = 118°

        Angle S = 5*6 + 1 = 31°

Ver imagen Blacklash
lublana

Answer:

x=6

[tex]\angle Q=\angle S=31^{\circ}[/tex]

[tex]\angle R=118^{\circ}[/tex]

Step-by-step explanation:

We are given that in triangle QRS

[tex]\angle Q=8x-17[/tex]

[tex]\angle R=19x+4[/tex]

[tex]\angle S=5x+1[/tex]

[tex]QR\cong RS[/tex]

We have to find the value of x and the measure of each angle

We know that congruent sides make congruent angles

Therefore, [tex]\angle Q=\angle S[/tex]

[tex]8x-17=5x+1[/tex]

[tex]8x-5x=1+17[/tex]

[tex]3x=18[/tex]

[tex]x=\frac{18}{3}=6[/tex]

Substitute the value of x

[tex]\angle Q=8(6)-17=31^{\circ}[/tex]

[tex]\angle R=19(6)+4=118^{\circ}[/tex]

[tex]\angle S=5(6)+1=31^{\circ}[/tex]