If HI≅HK and m∠HJK=59°, what is m∠IJK?
Since HI ≅ HK, this means that IJ is an angle bisector. Therefore, m∠IJK= m∠HJK/2 = 59°/2 = <<59/2=29.5>>29.5°.
Since HI is congruent to HK, we can assume that triangle HIJ is an isosceles triangle.
In an isosceles triangle, the base angles are congruent. Thus, m∠HIJ = m∠HJI.
Since the sum of the angles in a triangle is 180°, we can find m∠HIJ by subtracting the given angle from 180°.
m∠HIJ = 180° - m∠HJK
m∠HIJ = 180° - 59°
m∠HIJ = 121°
Since m∠HIJ = m∠HJI, m∠IJK is also 121°.
To find the measure of angle IJK, we need to use the fact that HI is congruent to HK and the given measure of angle HJK.
First, let's review what it means for two line segments to be congruent. When we say that HI is congruent to HK, it means that the lengths of HI and HK are equal.
Now, let's look at the given information. We know that m∠HJK is 59°. Since HI is congruent to HK, we can conclude that triangle HIJ is an isosceles triangle (a triangle with two congruent sides).
In an isosceles triangle, the angles opposite the congruent sides are also congruent. So, angle IHJ is congruent to angle IKJ.
Now, let's represent angle IJK as x°. Since angles in a triangle add up to 180°, we can write the equation:
m∠IHJ + m∠HIJ + m∠IJK = 180°
Substituting the congruent angles, we have:
x° + 59° + x° = 180°
Combining like terms, we get:
2x + 59 = 180
Subtracting 59 from both sides, we have:
2x = 121
Dividing both sides by 2, we get:
x = 60.5
Therefore, the measure of angle IJK is 60.5°.