Question

Whats the answer to these?

Answer 1

6.

• x = 15
• m∠CDF = 59°
• m∠FDE = 73°
• m∠CDE = 132°

7.

• m∠LMP = 74°
• m∠NMP = 63°

Explanation:

Question no. 6:

Given:

m∠CDF = (3x + 14)°

m∠FDE = (5x - 2)°

m∠CDE = (10x - 18)°

Since m∠CDE is sum of two angle m∠FDE and m∠CDF.

We can write it as:

m∠CDE = m∠FDE + m∠CDF

Substitute the value:

(10x - 18)° = (5x - 2)° + (3x + 14)°

10x - 18 = 5x - 2 + 3x + 14

Simplify like terms:

10x - 18 = 8x + 12

Subtract 8x on both sides:

10x - 18 - 8x = 8x + 12 - 8x

2x - 18 = 12

Add 18 on both sides:

2x - 18 + 18 = 12 + 18

2x = 30

Divide both sides by 2.

`\sf(2x)/(2)=(30)/(2)`

x = 15

Now, finding the value of the angle by substituting the value of x and simplifying it.

m∠CDF = (3 × 15 + 14)° = 59°

m∠FDE = (5 × 15 - 2)° = 73°

m∠CDE = (10 × 15 - 18)° = 132°

Question no. 7:

Given:

m∠LMP = m∠NMP + 11°

m∠NML = 137°

Since m∠NML is sum of two angle m∠LMP and m∠NMP.

We can write it as:

m∠NML = m∠LMP+ m∠NMP

Substitute the value:

137° = m∠NMP + 11° + m∠NMP

Simplify like terms:

137° = 2 m∠NMP + 11°

Subtract 11° on both sides:

137° - 11° = 2 m∠NMP + 11° - 11°

126° = 2 m∠NMP

Divide both sides by 2.

`\sf(126^\circ)/(2)=(2m\angle NMP)/(2)`

m∠NMP = 63°

Now, finding the value of the angle by substituting the value of m∠NMP and simplifying it.

m∠LMP = 63° + 11° = 74°