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The measures of the angles of △ABC are given by the expressions in the table. Angle Measure A 48° B (6x−28)° C (2x)° Find the value of x. Then find the measures of angles B and C. Enter your answers in the boxes. x = ​ m∠B= ​ 48 º ​ m∠C= ​ 12 º

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wolf1728

A 48°

B (6x−28)°

C (2x)°


48 + 6x -28 + 2x = 180 degrees


8x = 160 degrees


x = 20


angle B = 6x - 28 = 92


angle C = 2x = 40


Double-Check

Angle A + B + C = 48 + 92 + 40


Angle A + B + C = 180 degrees



calculista

Answer:

Part 1) the value of x is [tex]20\°[/tex]  

Part 2) [tex]m<B=92\°[/tex]

Part 3) [tex]m<C=40\°[/tex]

Step-by-step explanation:

Part 1)

Find the value of x

we know that

The sum of the internal angles of a triangle must be equal to [tex]180\°[/tex]

so

In this problem

[tex]m<A+m<B+m<C=180\°[/tex]

substitute the values

[tex]48\°+(6x-28)\°+(2x)\°=180\°[/tex]

solve for x

[tex]8x+20\°=180\°[/tex]

[tex]8x=180\°-20\°[/tex]

[tex]x=160\°/8=20\°[/tex]  

Part 2) Find the measure of angle B

[tex]m<B=(6x-28)\°[/tex]

substitute the value of x

[tex]m<B=(6(20)-28)\°=92\°[/tex]

Part 3) Find the measure of angle C

[tex]m<C=(2x)\°[/tex]

substitute the value of x

[tex]m<C=2(20)\°=40\°[/tex]

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