if BD is perpendicular to AC M angle DBE equals 2x - 1 + m angle CBE equals 5x - 42 find the value of x
1 answer:
<h2>Answer:</h2><h2>Step-by-step explanation:</h2>
I've drawn a graph in order to a better understanding of this problem. We know that:
BC is perpendicular to AC
∠DBE = 2x - 1
∠CBE = 5x - 42
Let's call the intersection of line BC and AC the point P, so:
∠P=90°
And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:
∠PCB = ∠CBE = 5x - 42
Moreover:
∠PBC = 2x - 1 - (5x - 42)
∠PBC = 2x - 1 - 5x + 42
∠PBC = -3x + 41
The internal angles of any triangle add up to 180°. Hence for ΔBPC:
90° + ∠PBC + ∠PCB = 180°
90° - 3x + 41 + 5x - 42 = 180°
2x + 89 = 180
2x = 91
x = 45.5°
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Kathleen must get 300 signatures to make sure she will have enough valid signatures for the crosswalk
<em><u>Solution:</u></em>
Given that Kathleen needs 240 valid signatures on a petition to get a crosswalk installed on her street
She knows that about 20% of the signatures will not be valid for a variety of reasons
Let "x" be the number of signatures
invalid signature = 20 % of x
valid signatures = 240
Then, according to question,
total number of signatures - invalid signatures = 240
x - 20 % of x = 240
Therefore, she must get 300 signatures so that she will have enough valid signatures for the crosswalk