Triangle jkl is isosceles. the measure of angle j is 72° and the measure of angle k is 36°. which statement describes angle l?

angle l is a base angle and measures 36°.
angle l is a base angle and measures 72°.
angle l is a vertex angle and measures 36°.
angle l is a vertex angle and measures 72°.

option (2) is correct.

Angle L is a base angle and measures 72°.

Step-by-step explanation:

Given : Triangle JKL is isosceles. The measure of angle J is 72° and the measure of angle K is 36°.

We have to choose the statement that correctly describes angle L.

ANGLE SUM PROPERTY of a triangle states that the sum of angle of a triangle is always 180°

Using angle sum property, we have,

⇒ ∠J + ∠K + ∠L = 180°

Substitute the values, we get,

⇒  72° + 36°  + ∠L = 180°

⇒  108°  + ∠L = 180°

⇒   ∠L = 180° - 108°

⇒   ∠L = 72°

In an isosceles triangle, two base angles are always equal.

Thus, L forms a base angle with measure 72°

Hence, option (2) is correct.

right

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.