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Geometry :)


pls help! thank you soo much :)
( image attached)

Geometry :) pls help! thank you soo much :) ( image attached)-example-1
User Moubeen Farooq Khan
by
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1 Answer

22 votes
22 votes

Answer:

m∠ABC = 81°

m∠FEC = 90°

Explanation:

A median of a triangle is a line segment from the vertex to the mid-point of the side opposite that vertex.

If AB ≅ BC then triangle ABC is an isosceles triangle.

Therefore, if BE is the median of triangle ABC, then m∠ABE ≅ m∠CBE.

Therefore, the measure of ∠ABC is twice the measure of ∠ABE.

First, convert the given measure of ∠ABE into decimal degrees.


\boxed{\textsf{Decimal degrees}=\sf Degrees + (Minutes)/(60)+ (Seconds)/(3600)}


\begin{aligned}\implies \angle ABE=40^(\circ)30'&=40+(30)/(60)+(0)/(3600)\\&=40+0.5+0\\&=40.5^(\circ)\end{aligned}

Therefore, m∠ABE = 40.5°.

If m∠ABC is twice the measure of ∠ABE:


\begin{aligned}\implies m \angle ABC&=2 * \angle ABE\\&=2 * 40.5^(\circ)\\&=81^(\circ)\end{aligned}

As triangle ABC is an isosceles triangle where AB≅BC, the median BE is perpendicular to AC. Therefore, m∠FEC = 90°.

Geometry :) pls help! thank you soo much :) ( image attached)-example-1
User Jason Turan
by
2.8k points