Question

1. in the figure, m∠1 = m∠2 = 22 and m∠3 = m∠4 = 123. from this, you can conclude that m∠tkl

35
57
47
22

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle TKL\), we know that \(\angle3\) is an exterior - angle. By the exterior - angle property of a triangle, an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's consider \(\triangle TKL\), where \(\angle3\) is an exterior angle and \(\angle1\) and \(\angle TKL\) are the non - adjacent interior angles.

Step2: Calculate \(\angle TKL\)

We know that \(\angle3 = 123^{\circ}\) and \(\angle1=22^{\circ}\). Using the exterior - angle formula \(\angle3=\angle1 + \angle TKL\), we can find \(\angle TKL\) as \(\angle TKL=\angle3-\angle1\). Substituting the given values: \(\angle TKL = 123 - 22=101^{\circ}\). But we want to find the angle in the other part of the figure. Let's consider the fact that we can also use the angle - sum property in a different way. In the overall figure, we know that in a triangle - related context. Another way is to note that in the relevant triangle, if we consider the relationship between the given angles. Since \(\angle3\) and the angle adjacent to \(\angle TKL\) (let's call it \(\angle x\)) form a linear pair (sum to 180°), the angle adjacent to \(\angle TKL\) is \(180 - 123=57^{\circ}\). In the smaller triangle with \(\angle2\), using the angle - sum property of a triangle. Let the angle we want to find be \(\theta\). We know that the sum of angles in a triangle is 180°. If we consider the triangle with \(\angle2\) and the angle adjacent to \(\angle TKL\), we have \(\theta=180-(22 + 101)=57^{\circ}\).

Answer:

57