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:
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~~
