Question

homework 3.2-parallel lines and transversals
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5 of 6 02:11
consider the diagram shown. find m∠amb.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. Angle $\angle JIL$ and the $70^{\circ}$ angle are vertical - angles, so $m\angle JIL = 70^{\circ}$. Also, angle $\angle KLM$ and the $110^{\circ}$ angle are vertical - angles, so $m\angle KLM=110^{\circ}$.

Step2: Use the property of a straight - line angle

A straight - line angle is $180^{\circ}$. Consider the straight line $HL$. At point $I$, the angles around point $I$ on line $HL$ satisfy the angle - sum property.

Step3: Find the angle adjacent to $\angle JIL$

The angle adjacent to $\angle JIL$ on line $HL$ is $180 - 70=110^{\circ}$.

Step4: Use the angle - sum property of a triangle

In the triangle formed by the intersection of the lines at $M$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let's consider the triangle with one vertex at $M$. We have two of the angles related to the angles formed by the parallel lines and transversals.
The two angles that meet at $M$ (adjacent to the angles on the parallel - line transversal intersections) and $\angle AMB$ form a triangle. Since the two non - $\angle AMB$ angles in the triangle are parts of the linear pairs and vertical - angle relationships, we know that $\angle AMB = 70^{\circ}$.

Answer:

$70^{\circ}$