The measure of angle JKL can be represented using the expression 3x + 5. Point K has three lines extending from it. One line extends to point J, another to point M, and the other to point L. Angle J K M is 45 degrees. Angle M K L is x degrees. What is the degree measure of Angle JKL? °
The correct answer and explanation is:
Let’s break down the problem step-by-step:
Given:
- Point K has three lines extending to points J, M, and L.
- Angle JKL is represented by the expression 3x+53x + 5.
- Angle JKM measures 45∘45^\circ.
- Angle MKL measures x∘x^\circ.
Goal:
Find the degree measure of angle JKL.
Step 1: Understand the angles around point K
The three lines from point K to points J, M, and L create three adjacent angles around K:
- Angle JKM=45∘JKM = 45^\circ
- Angle MKL=x∘MKL = x^\circ
- Angle JKL=3x+5JKL = 3x + 5 (this is the angle between line KJ and KL)
From the naming of the angles, it appears the three angles around K formed between the rays KJ, KM, and KL are:
- ∠JKM=45∘\angle JKM = 45^\circ
- ∠MKL=x∘\angle MKL = x^\circ
- ∠JKL=?\angle JKL = ? (but the problem states it equals 3x+53x + 5)
However, note that JKL is an angle formed between points J-K-L. It appears that ∠JKL\angle JKL is the sum of ∠JKM\angle JKM and ∠MKL\angle MKL, i.e.: ∠JKL=∠JKM+∠MKL\angle JKL = \angle JKM + \angle MKL
So, 3x+5=45+x3x + 5 = 45 + x
Step 2: Solve the equation
3x+5=45+x3x + 5 = 45 + x
Subtract xx from both sides: 3x−x+5=453x – x + 5 = 45 2x+5=452x + 5 = 45
Subtract 5 from both sides: 2x=402x = 40
Divide both sides by 2: x=20x = 20
Step 3: Calculate angle JKLJKL
Recall, ∠JKL=3x+5=3(20)+5=60+5=65∘\angle JKL = 3x + 5 = 3(20) + 5 = 60 + 5 = 65^\circ
Final answer:
65∘\boxed{65^\circ}
Explanation:
In this problem, point K is the vertex where three rays or lines extend to points J, M, and L. The angles formed at K are adjacent, and the sum of the smaller angles ∠JKM\angle JKM and ∠MKL\angle MKL equals the larger angle ∠JKL\angle JKL, which is represented algebraically as 3x+53x + 5.
By setting up the equation 3x+5=45+x3x + 5 = 45 + x, we find the value of xx, which is the unknown angle measure of ∠MKL\angle MKL. Once xx is found, substituting it back into the expression for ∠JKL\angle JKL gives us the degree measure of ∠JKL\angle JKL.
Thus, the angle ∠JKL\angle JKL measures 65 degrees.