Question

JKL is a straight line.

JK = KL = KM.
Angle KLM = 58°
Work out the size of the angle marked x.
Give a reason for each stage of your working.
КІ
Х
M
I
580
L
Total marks: 4
Matha Watch Lid
Terms

Answer 1

x = 32°

Explanation:

∆KLM is an isosceles triangle because it has two equal sides, KL & KM. Therefore, the angles opposite to each of the two equal sides, which are referred to as the base angles are congruent to each other.

m<KML = m<KLM = 58°

m<MKL = 180 - (58 + 58) (Sum of triangle)

m<MKL = 64°

m<JKM = 180 - m<MKL (linear pair theorem)

m<JKM = 180 - 64 (Substitution)

m<JKM = 116°

∆JKM is also an isosceles triangle with two equal sides. Therefore, it's based angles (x & <J) would also be equal to each other.

Thus:

x = ½(180 - m<JKM)

x = ½(180 - 116) (Substitution)

x = 32°