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TiliK225
2 months 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:
zzz [12.3K]2 months ago
7 0
Please refer to the image provided below.

Svet_ta [12.7K]2 months ago
5 0

Result: The angle ABD measures 148°.

Explanation step-by-step: Given that ray BD bisects angle CBE, and ray BC aligns with ray BA.

Additionally,

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

We are tasked with determining the measurement of angle ABD.

Since ray BD bisects angle CBE, 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.

Therefore, we conclude

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

Consequently, the measure of angle ABD is thus 148°.

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