Let's begin noting that a triangle is isosceles if and only if two of its angles are congruent. We can thus find the angle <ABP, recalling that the sum of the interior angles of a triangle is equal to 180°.
Finally, let point K be the intersection between segments BC and PQ, and let's note that the triangle PQB is a right isosceles triangle, since all the angles in a square are equal to 90°, and the two triangles APB and BQC are congruent.
Therefore, the angle BKQ is equal to 180-50-45=85°.
Of course angle BKP=180-85=95°.
Hope this helps :)
Answer:
x ≈ - 5.32, x ≈ 1.32
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± 
( subtract 2 from both sides )
x = - 2 ±
Thus
x = - 2 - ≈ - 5.32 ( to 2 dec. places )
x = - 2 + ≈ 1.32 ( to 2 dec. places )
B, it’s the point that the lines cross
Question 11a)
We are given side BC equals to side CE and angle CBA equals to angle CED
We also know that angle ACB equals to angle ECD are equal (opposite angles properties)
We have enough information to deduce that triangle ABC and triangle CDE are equal by postulate Angle-Side-Angle (ASA)
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Question 11b)
We are given side AB equal to side ED, side BC equals to side EF, and side AC equals to side DF
We have enough information to deduce that triangle ABC and triangle DEF congruent by postulate Side-Side-Side (SSS)
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Question 11c)
We are given side AC equals to side DF, angle ABC equals to angle DEF, and angle BAC equals to angle EDF
We have enough information to deduce that triangle ABC congruent to triangle DEF by postulate Angle-Side-Angle (ASA)
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Question 11d)
We do not have enough information to tell whether this shape congruent or not
Answer: each salesperson sold 89 cars last year.
Step-by-step explanation:
The total number of sales people at the dealership shop is 13.
Last year they each sold the same number of cars. The total number of cars that they sold together last year was 1157. Therefore, the number of cars that each salesperson sold would be
Total number of cars sold/ number of salespersons
It becomes
1157/13 = 89
