Question

1. Given ℓ || n. If m∠12 = 5x + 10 and m∠14 = 6x − 4, then x = ? and m∠4 = ?.

2. Given ℓ || n. If m∠14 = 75°, then m∠2 = ?.
3. Given ℓ || n. If m∠9 = 3x + 12 and m∠15 = 2x + 27, then x = ? and m∠10 = ?.
4. Given ℓ || n. If m∠16 = 5x + 18 and m∠15 = 3x + 2, then x = ? and m∠8 = ?.

Answer 1

1. x = 14, m∠14 = 80. 2. m∠2 = 75°. 3. x = 15, m∠10 = 57. 4. x = -8, m∠8 = -22.

Step-by-step explanation:

1. Given ℉ || n. If m∠12 = 5x + 10 and m∠14 = 6x − 4, then x = ? and m∠14 = ?

To find the value of x, we can equate the two given angles:

5x + 10 = 6x − 4

Simplifying the equation, we get:

10 + 4 = 6x − 5x

14 = x

So, x = 14.

Now, to find the value of m∠14, we substitute the value of x in either angle equation:

m∠14 = 6x − 4 = 6(14) − 4 = 84 − 4 = 80

Therefore, x = 14 and m∠14 = 80.

2. Given ℉ || n. If m∠14 = 75°, then m∠2 = ?

Since ℉ || n, m∠14 and m∠2 are corresponding angles, which means they are equal. Therefore, m∠2 = 75°.

3. Given ℉ || n. If m∠9 = 3x + 12 and m∠15 = 2x + 27, then x = ? and m∠10 = ?

To find the value of x, we can equate the two given angles:

3x + 12 = 2x + 27

Simplifying the equation, we get:

x = 15

So, x = 15.

Now, to find the value of m∠10, we substitute the value of x in either angle equation:

m∠10 = 3x + 12 = 3(15) + 12 = 45 + 12 = 57

Therefore, x = 15 and m∠10 = 57.

4. Given ℉ || n. If m∠16 = 5x + 18 and m∠15 = 3x + 2, then x = ? and m∠8 = ?

To find the value of x, we can equate the two given angles:

5x + 18 = 3x + 2

Simplifying the equation, we get:

2x = -16

x = -8

So, x = -8.

Now, to find the value of m∠8, we substitute the value of x in either angle equation:

m∠8 = 5x + 18 = 5(-8) + 18 = -40 + 18 = -22

Therefore, x = -8 and m∠8 = -22.