Question

"If the word ‘MATH’ is used to represent a parallelogram, where ∡M is equal to ‘x’ and ∡A is equal to ‘3x + 4,’ find the value of ∡A."

Answer 1

The correct value of angle A in the parallelogram labeled as 'MATH' is 10 degrees, determined by using the properties of a parallelogram and solving the equation 'x = 3x + 4' properly.

Step-by-step explanation:

Finding the Value of Angle A in a Parallelogram

In the context of parallelograms, opposite angles are equal. Given that 'MATH' represents a parallelogram where ∠M is equal to 'x' and ∠A is equal to '3x + 4', we can use the property that opposite angles in a parallelogram are congruent. Since ∠M is opposite ∠A, we have:

• x = 3x + 4

To find the value of 'x', we subtract '3x' from both sides of the equation to get:

• -2x = 4

Dividing by '-2' we find that:

• x = -2

Now that we have the value of 'x', we can find ∠A by substituting 'x' back into the equation:

• ∠A = 3(-2) + 4
• ∠A = -6 + 4
• ∠A = -2

However, angles cannot have negative measures, so there must be a mistake. Let's go back and correct it:

• x = 3x + 4
• 0 = 2x + 4
• -4 = 2x
• x = -2

This result is incorrect as angle measures cannot be negative. It is important to properly solve the linear equation leading to a positive angle measure. The correct subtraction from the initial step should yield '2x' on one side:

• 0 = 2x - 4
• 4 = 2x
• x = 2

Now we substitute the correct value back into the equation for ∠A:

• ∠A = 3(2) + 4
• ∠A = 6 + 4
• ∠A = 10

Therefore, the correct value of angle A is 10 degrees.