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elixir [45]
3 years ago
11

If ray BD bisects angle CBE, ray BC is transparent to ray BA, angle CBD = (3x + 25) degrees, and angle DBE = (7x - 19) degrees,

find angle ABD

Mathematics
2 answers:
Alex777 [14]3 years ago
7 0
Check the picture below.

Alenkasestr [34]3 years ago
5 0

Answer:  The required measure of angle ABD is 148°.  

Step-by-step explanation:  Given that ray BD bisects angle CBE, ray BC is transparent to ray BA.

Also,

m\angle CBD=(3x+25)^\circ,~~m\angle DBE=(7x-19)^\circ,~~m\angle ABC=90^\circ.

We are to find the measure of angle ABD.

Since ray BD bisects angle CBE, so we have

m\angle CBD=m\angle DBE\\\\\Rightarrow (3x+25)^\circ=(7x-19)^\circ\\\\\Rightarrow 3x+25=7x-19\\\\\Rightarrow 7x-3x=25+19\\\\\Rightarrow 4x=44\\\\\Rightarrow x=\dfrac{44}{4}\\\\\Rightarrow x=11.

So, we get

m\angle CBD=(3\times11+25)^\circ=58^\circ.

Therefore,

m\angle ABD=m\angle ABC+m\angle CBD=90^\circ+58^\circ=148^\circ.

Thus, the required measure of angle ABD is 148°.  

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