Question

JKL is a straight line
JK=KL=KM
Angle KLM=58 degrees
work out the size of the angle marked x
Give one reason for each stage of your working

Answer 1

Given : JKL is a straight line

JK=KL=KM

Angle KLM=58°

To Find :  size of the angle marked x

Solution:

in Δ KLM

KL = KM

=> ∠KLM = ∠KML

=> ∠KML = 58°

in Δ KJM

JK = KM

=> ∠KJM = ∠KMJ

=>  ∠KJM = ∠KMJ = x

in  Δ JLM

∠JLM + ∠LMJ + ∠LJM = 180°

=> ∠KLM + ∠KML + ∠KMJ + ∠KJM = 180°

=> 58° + 58° + x + x=  180°

=>  58° + x  = 90°

=> x= 32°

Value of x = 32°

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