Question

Triangle g h i and triangle j k l are shown. angle l and angle i are congruent. angle j and g are congruent to each other. angle k and angle h are right angles. if m∠j = 44°, what is m∠i?

1) 2°
2) 44°
3) 46°
4) 90°

Answer 1

In the described triangles, since angle j is 44° and triangle jkl has a right angle at k, the other angle l must be 46°, so angle i, being congruent to angle l, is also 46°. So, the correct answer is 3) 46°.

Step-by-step explanation:

If triangle ghi and triangle jkl have congruent angles such that angle l and angle i are congruent and angle j and angle g are congruent, and we know that angle k and angle h are right angles, then we can use the fact that the sum of angles in a triangle is always 180 degrees.

Given that m°j = 44°, we can find m°i by recognizing that triangle jkl is isosceles with two angles being 44 degrees because angle j is congruent to angle g and thus m°j = m°g.

Since angle k is a right angle (90 degrees), the remaining angle l must be 180 - 90 - 44 = 46°.

Because angle l and angle i are congruent, m°i also equals 46 degrees.

So, the correct answer is 3) 46°.