Final answer:
In rectangle KLMN, if m∠1 = 37°, we can find m∠3, m∠2, and m∠4 by using the properties of opposite angles. The measure of angle m∠3 is 143°, the measure of angle m∠2 is also 143°, and the measure of angle m∠8 is 37°.
Step-by-step explanation:
In rectangle KLMN, the sum of the measures of opposite angles is 180° because all angles in a rectangle are right angles. This means that m∠1 + m∠3 = 180° and m∠2 + m∠4 = 180°.
Since m∠1 is given as 37°, we can substitute this value into the equation m∠1 + m∠3 = 180° to find m∠3. So, 37° + m∠3 = 180°. Subtracting 37° from both sides gives m∠3 = 180° - 37°, which simplifies to m∠3 = 143°.
Similarly, we can find m∠2 by substituting the given value for m∠1 into the equation m∠2 + m∠4 = 180°. So, 37° + m∠4 = 180°. Subtracting 37° from both sides gives m∠4 = 180° - 37°, which simplifies to m∠4 = 143°.
To find m∠8, we need to use the fact that opposite angles are congruent. So, m∠1 = m∠8, which means m∠8 is also 37°.