Question

HELPPP!!!! 10 PTS!!

Find the missing information

x = _____ m angle A = ____

Answer 1

x = 21.25

Angle A = 68.75

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)

Answer 2

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

`2x+(3x+5)+(3x+5)=8x+10=180 \iff 8x=170 \iff x=(170)/(8)=(85)/(4)`

So, angle A measures

`3\left((85)/(4)\right)+5 = (275)/(4)`