Question

In the rectangle KLMN, if m∠1 = 37°, find the following angles:

a) m∠8
b) m∠2
c) m∠4
d) m∠3

Answer 1

a) m∠8 = 37°

b) m∠2 = 143°

c) m∠4 = 143°

d) m∠3 = 37°

Step-by-step explanation:

Given that m∠1 = 37°, we can find the other angles:

a) m∠8 (opposite angle to ∠1): m∠8 = m∠1 = 37°

b) m∠2 (adjacent angle to ∠1): m∠2 = 180° - m∠1 = 180° - 37° = 143°

c) m∠4 (opposite angle to ∠2): m∠4 = m∠2 = 143°

d) m∠3 (adjacent angle to ∠2): m∠3 = 180° - m∠2 = 180° - 143° = 37°

So, the angles are:

a) m∠8 = 37°

b) m∠2 = 143°

c) m∠4 = 143°

d) m∠3 = 37°

Answer 2

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°.