Respuesta :

The triangle is isosceles, so the bottom angles have the same measure. So, the angles measure 2x, 3x+5 and 3x+5.

The sum of the interior angles of a triangle is 180, so we have

[tex]2x+(3x+5)+(3x+5)=8x+10=180 \iff 8x=170 \iff x=\dfrac{170}{8}=\dfrac{85}{4}[/tex]

So, angle A measures

[tex]3\left(\dfrac{85}{4}\right)+5 = \dfrac{275}{4}[/tex]

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Answer:

x = 21.25

Angle A = 68.75

Step-by-step explanation:

This is an isosceles triangle because two sides are congruent. So angle A is equal to angle C

(3x + 5) + (3x + 5) + 2x = 180

3x + 5 + 3x + 5 + 2x = 180

3x + 3x + 2x + 5 + 5 = 180

8x + 10 = 180

8x = 180 - 10

8x = 170

x = 170 ÷ 8

x = 21.25

Angle A = 3x + 5

3x + 5

3(21.25) + 5

63.75 + 5

= 68.75

Check.

68.75 + 68.75 + 2(21.25) = 180

137.5 + 2(21.25) = 180

137.5 + 42.5 = 180

180 = 180

(Correct)

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