Question

Pls help me with these 2 math questions

Answer 1

**Problem 1:**

`- \( m\angle A = (3 * 19 + 18)^\circ = 75^\circ \) ;- \( m\angle B = (7 * 19 - 58)^\circ = 75^\circ \) ;- \( m\angle C = (2 * 19 - 8)^\circ = 32^\circ \)`

**Problem 2:**

-
`\( KL = 9 * (3)/(2) - 40 = -31 \)` (Note: This result indicates that the given values may not form a valid triangle, as side lengths cannot be negative.)

-
`\( LM = 7 * (3)/(2) - 37 = -28.5 \)` (Note: This result indicates that the given values may not form a valid triangle, as side lengths cannot be negative.)

-
`\( KM = 3 * (3)/(2) + 23 = (29)/(2) \)`





**Problem 1:**

Given triangle
`\( \Delta ABC \) with \( \overline{AC} \cong \overline{CB} \)`:

`- \( m\angle A = (3x + 18)^\circ \)- \( m\angle B = (7x - 58)^\circ \)- \( m\angle C = (2x - 8)^\circ \)`

We know that the sum of the interior angles of a triangle is
`\(180^\circ\)`, so:

`\[ m\angle A + m\angle B + m\angle C = 180^\circ \]`

Substitute the given expressions:

`\[ (3x + 18) + (7x - 58) + (2x - 8) = 180 \]`

Combine like terms:

`\[ 12x - 48 = 180 \]`

Add 48 to both sides:

`\[ 12x = 228 \]`

Divide by 12:

`\[ x = 19 \]`

Now, substitute \(x\) back into the angle expressions:

`- \( m\angle A = (3 * 19 + 18)^\circ = 75^\circ \) ;- \( m\angle B = (7 * 19 - 58)^\circ = 75^\circ \) ;- \( m\angle C = (2 * 19 - 8)^\circ = 32^\circ \)`

**Problem 2:**

Given triangle
`\( \Delta KLM \)`:

`- \( \angle K \cong \angle L \)`

`- \( KL = 9x - 40 \)`

`- \( LM = 7x - 37 \)`

`- \( KM = 3x + 23 \)`

Since
`\( \angle K \cong \angle L \)`, it's an isosceles triangle, and the two sides opposite these angles are congruent. Therefore, KL = LM:

`\[ 9x - 40 = 7x - 37 \]`

Subtract 7x from both sides:

`\[ 2x - 40 = -37 \]`

Add 40 to both sides:

`\[ 2x = 3 \]`

Divide by 2:

`\[ x = (3)/(2) \]`

Now, substitute x back into the expressions:

-
`\( KL = 9 * (3)/(2) - 40 = -31 \)` (Note: This result indicates that the given values may not form a valid triangle, as side lengths cannot be negative.)

-
`\( LM = 7 * (3)/(2) - 37 = -28.5 \)` (Note: This result indicates that the given values may not form a valid triangle, as side lengths cannot be negative.)

-
`\( KM = 3 * (3)/(2) + 23 = (29)/(2) \)`