Determine the value of ∠OMP.

m∠OMP = _ degrees

The angle J formed from the two secants is half the difference of the subtended arcs, J = (1/2) (arc PN - arc KL).

30 = (1/2) (81 - KL)

60 = 81 - KL

KL = 81 - 60 = 21 degrees

The two vertical angles, OMP and KML, add up to the two subtended arcs, KL and OP.  Since the vertical angles are congruent,

2 ∠OMP = 57 + 21 = 78

∠OMP = 39 degrees

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc