SM=3x−4, and RN=9x−20. Find the value of x
1 answer:
Answer:
Option (A).
Step-by-step explanation:
Given question is incomplete; find the complete question with the attachment.
In the triangle NRL,
Points P, S and M are the midpoints of the sides NR, RL and LN respectively.
Sides SM = (3x - 4), NR = (9x - 20)
By the theorem of midpoints in a triangle,
SM =
(3x - 4) =
6x - 8 = 9x - 20
9x - 6x = 20 - 8
3x = 12
x = 4
Therefore, Option (A) will be the answer.
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Answer:
m∠WXZ = 38°
m∠ZXY = 52°
Step-by-step explanation:
In the question
- ∠WXZ and ∠ZXY are two adjacent angles and formed together ∠WXY
- That means the measure of ∠WXY equal the sum of measures of ∠WXZ and ∠ZXY
∵ ∠WXY is a right angle
→ That means its measure is 90°
∴ m∠WXY = 90°
∵ m∠WXZ + m∠ZXY = m∠WXY
∵ m∠WXZ = (5x + 3)°
∵ m∠ZXY = (8x - 4)°
∵ m∠WXY = 90°
→ Substitute their values in the equation above
∴ (5x + 3) + (8x - 4) = 90
→ Add the like terms in the left side
∵ (5x + 8x) + (3 - 4) = 90
∴ 13x + (-1) = 90
∴ 13x - 1 = 90
→ Add 1 to both sides
∴ 13x - 1 + 1 = 90 + 1
∴ 13x = 91
→ Divide both sides by 13
∴
∴ x = 7
→ To find the measure of each angle substitute x by 7 in their measures
∵ m∠WXZ = 5x + 3
∴ m∠WXZ = 5(7) + 3
∴ m∠WXZ = 35 + 3
∴ m∠WXZ = 38°
∵ m∠ZXY = 8x - 4
∴ m∠ZXY = 8(7) - 4
∴ m∠ZXY = 56 - 4
∴ m∠ZXY = 52°