Answer:
∠ 1 = 123°
Step-by-step explanation:
One way
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 1 is an external angle of the triangle, thus
∠ 1 = 90° + 33° = 123°
Second way
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle in Δ
third angle = 180° - (90 + 33)° = 180° - 123° = 57°
The third angle and ∠ 1 form a straight angle and are supplementary, thus
∠ 1 = 180° - 57° = 123°
Answer:
Opposite angles are congruent
Step-by-step explanation:
The parallelogram has parallel opposite sides and also the opposite sides are congruent. Few other properties of parallelogram are -
- It has two pairs of parallel opposite sides.
- Its diagonals bisect each other.
- It has two pairs of equal opposite angles.
- It has two pairs of equal and parallel opposite sides.
So, the answer is D.) opposite angles are congruent.
Answer:
y = -4x - 38
Step-by-step explanation:
Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = -4x + 1 is -4. Substitute m = -4 and the point (-9,-2) into the point slope form of a line.

Apply the distributive property to find the slope intercept form.
y + 2 = -4(x+9)
y + 2 = -4x - 36
y = -4x - 38
Answer:
The transformation is 5 units left and 4 units down
<u>It is described as the rule:</u>
or
Answer:
24.03 units (nearest hundredth)
Step-by-step explanation:
The distance between B and A is: AB = AH + HB
We have been given AH, so we just need to find the measure of HB.
First, find the angle AOH using tan trig ratio:

where:
is the angle- O is the side opposite the angle
- A is the side adjacent the angle
Given:
= ∠AOH- O = AH = 8
- A = OH = 19.80


∠BOA = ∠BOH + ∠AOH
⇒ ∠BOH = ∠BOA - ∠AOH
⇒ ∠BOH = 61° - 22.00069835°
= 38.99930165°
Now we can find HB by again using the tan trig ratio:
Given:
= ∠BOH = 38.99930165°- O = HB
- A = OH = 19.80
Substituting given values:



Therefore:
AB = AH + BH
⇒ AB = 8 + 16.03332427
= 24.03 units (nearest hundredth)