Answer :

By using the given angle ratio, linear pairs, vertically opposite angles, and the properties of parallel lines and transversals, we determined the measures of the angles in the figure:

∠1 = ∠3 = ∠5 = ∠7 = 72°

∠2 = ∠4 = ∠6 = ∠8 = 108°

In the given problem, we start with the information that the ratio of angle measures is ∠1:∠2=∠2:∠3. Recognizing that ∠1 and ∠2 form a linear pair, we use the fact that the sum of their measures is 180 degrees:

∠1 + ∠2 = 180°

Substituting the given ratio, we get:

2x + 3x = 180°

Combining like terms:

5x = 180°

Solving for x:

x = 36°

With the value of x determined, we can calculate the measures of ∠1 and ∠2:

∠1 = 2x = 2(36°) = 72°

∠2 = 3x = 3(36°) = 108°

Next, we note that ∠1 and ∠3 are vertically opposite angles, so ∠1 = ∠3 = 72°. Similarly, ∠2 and ∠4 are vertically opposite angles, so ∠2 = ∠4 = 108°.

Additionally, given that line l is parallel to line m and t is a transversal, we can identify corresponding angles:

∠1 = ∠5 = 72°

∠2 = ∠6 = 108°

∠3 = ∠7 = 72°

∠4 = ∠8 = 108°

This comprehensive analysis helps us understand the relationships between angles in the figure based on the given information and geometric principles.

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The question probable may be:

In the figure, l∥m and a transversal t cuts them. If ∠1: ∠2: ∠3, find the measure of each of the marked angles.

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