If MNOP is a trapezoid and if MQ is congruent to NR and m<NMQ=166 degrees calculate <MNR
Since MQ and NR are congruent and parallel, we know that MNOR is a parallelogram. Therefore, we have:
∠MNR = ∠NOR (opposite angles of a parallelogram are congruent)
And we also know that:
∠NMQ + ∠QMN = 180° (the sum of the angles of a triangle is 180°)
Substituting the given value:
166° + ∠QMN = 180°
Solving for ∠QMN:
∠QMN = 14°
Now we can use the fact that MNOR is a parallelogram to find ∠NOR:
∠NOR = 180° - ∠QMN
∠NOR = 166°
Therefore, we have:
∠MNR = ∠NOR = 166°
what is the sum of the exterior angles of a nonagon
The sum of the exterior angles of any polygon is always 360 degrees.
Therefore, to find the sum of the exterior angles of a nonagon (a nine-sided polygon), we can use the formula:
Sum of exterior angles = 360 degrees
Since a nonagon has 9 sides, it also has 9 exterior angles. The exterior angles of any polygon are formed by extending one of its sides and its adjacent side. Since all the exterior angles of a nonagon are congruent (they have the same measure), we can divide 360 by 9 to find the measure of one exterior angle.
Sum of exterior angles of a nonagon = 360 degrees
Measure of one exterior angle of a nonagon = Sum of exterior angles of a nonagon / Number of sides of the nonagon
= 360/9
= 40 degrees
Therefore, each exterior angle of a nonagon has a measure of 40 degrees, and the sum of all nine exterior angles is 360 degrees.
the notation RY(arrow right) and YR(arrow right) represent the same ray true or false.
True.
The notation "RY →" and "YR →" both refer to the same ray. In both notations, the starting point of the ray is at point R, and the arrow indicates that the ray extends infinitely in the direction of point Y. The order of the points (RY or YR) does not affect the direction or the position of the ray. Therefore, "RY →" and "YR →" represent the same ray.
t/f
a rhombus with congruent diagonals is a square
False.
A rhombus with congruent diagonals is not necessarily a square. While a square is a type of rhombus with four congruent sides and four congruent angles, a rhombus does not require its angles to be 90 degrees.
It is true that a square has congruent diagonals, but not all rhombuses with congruent diagonals have congruent sides and 90-degree angles, which are the defining features of a square. Therefore, a rhombus with congruent diagonals is only guaranteed to be a square if it also has four congruent sides and 90-degree angles.