Question

In a parallelogram SCAN, s = 4x + 15° and a = 2x + 95°. Solve for x and the measure of the other angles.

Answer 1

x = 40

Explanation:

It is a property of parallelograms that the opposing angles are equal. Here, ∠A and ∠S are equal.

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Solving :

⇒ 4x + 15 = 2x + 95

⇒ 4x - 2x = 95 - 15

⇒ 2x = 80

⇒ x = 40

Answer 2

Parallelogram

In a parallelogram SCAN, s = 4x + 15° and a = 2x + 95°. Solve for x and the measure of the other angles.

In the parallelogram shown above, we can prove that ∠S = ∠A and ∠C = ∠N. Given that,

• ∠S = 4x + 15°
• ∠A = 2x + 95°

Since they are congruent, we can equate these two angle measurements to each other and simplify.

• ∠S = ∠A
• 4x + 15 = 2x + 95
• 4x - 2x = 95 - 15
• 2x = 80
• x = 40

The value of x is 40. We can now determine the measure of ∠S and ∠A by substituting the value of x to the variable x.

• ∠S
• 4x + 15
• 4(40) + 15
• 160 + 15
• 175

• ∠A
• 2x + 95
• 2(40) + 95
• 80 + 95
• 175

The values of ∠S and ∠A are 175°. Meanwhile, the relationship between ∠S and ∠C, and ∠N and ∠A are supplementary. Proving that ∠C = ∠N, we can find out the supplement of 175.

• ∠S + ∠C = 180
• ∠N + ∠A = 180

Given:

• ∠S = 175
• ∠A = 175

Solution:

• 175 + ∠C = 180
• ∠C = 180 - 175
• ∠C = 5°

• 175 + ∠N = 180
• ∠N = 180 - 175
• ∠N = 5°

Answer:

• The value of x is 40.
• The measure of ∠S and ∠A is 175°.
• The measure of ∠C and ∠N is 5°.

Wxndy~~