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= ​ º ​ m∠C= ​ º

Respuesta :

All three angles of a triangle must add up to 180°. If Angle A is 48° then 180-48=132.

Angles B and C have to add up to 132°. So we can set up an equation: (6x-28)+(2x)=132.

Drop parenthesis and combine like terms: 6x-28+2x=132
8x-28=132

Now we need to get x by itself so add 28: 8x=160

Divide by 8: x=20

Now that we now x, we can plug it in for B: 6(20)-28=92. Angle B is 92°.

Repeat for Angle C: 2(20)=40. Angle C is 40°.

To check, add all three angles together. If they equal 180, the numbers are right.

So: 48+92+40=180°.

Answer:

x = 20  ∠B = 92°  ∠C = 40°

Step-by-step explanation:

The sum of angles of a triangle is 180°.

48 +(6x -28) +2x = 180

8x +20 = 180

8x = 160

x = 20

∠B = (6x -28)° = (6*20 -28)° = 92°

∠C = 2x° = 40°

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