Question

find ( mangle jkm ).
the measure of ( angle jkm ) is ( square^{circ} ).

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(42^{\circ}+3x^{\circ}=(4x + 3)^{\circ}\)

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find \(m\angle JKM\)

Since \(\angle JKM\) and \((4x + 3)^{\circ}\) are supplementary (\(\angle JKM+(4x + 3)^{\circ}=180^{\circ}\)), substitute \(x = 39\) into \((4x + 3)\)
\(4x+3=4\times39 + 3=156+3=159\)
Then \(m\angle JKM=180-(4x + 3)=180 - 159=21\)

Answer:

\(21\)