The blue dot is at what value on the number line?
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The value of the variable x is found to be x = 9.
<h3>What is termed as angle bisector?</h3>- In geometry, an angle bisector is a line that divides an angle into two equal angles.
- A bisector is something that divides a shape or thing into two equal portions.
- An angle bisector is a ray that divides an angle into two equal components of the same measurement.
A bisected angle divides the two sides in equals.
JKM = LKM
As, both are equal.
Then, each of these angles are 1/2 the angle JKL.
1/2 JKL = MKL
1/2 ×( 92) = 5x + 1
Further simplifying;
46 = 5x+1
Subtract 1 from each side
46-1 = 5x
45 = 5x
Divide each side by 5
45/5 = 5x/5
x = 9
Thus, the value of the unknown variable is found to be x = 9 units.
To know more about the angle bisector, here
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Answer:
Step-by-step explanation:
<em><u>Given</u></em><u>:</u> A line m is perpendicular to the angle bisector of ∠A. We call this
intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.
AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.
<u><em>To Prove</em></u>: <em><u>ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are</u></em>
<em> </em><em><u>equal. </u></em>
<em><u>Solution</u></em>: Now, In ΔADM and ΔADN
∠MAD=∠NAD ...(1) (∵Given)
AD=AD ...(2) (∵common side)
∠ADM=∠ADN ...(3) (∵Given)
<u><em> Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN</em></u>
( ∵ ASA congruence rule)
⇒<u><em> AM=AN</em></u>
Now, In Δ AMN
AM=AN (∵ Proved)
Hence, ΔAMN is an isosceles triangle.
