Answered: for a sewing project tanya cut…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter10: Measurement, Area, And Volume

Section10.1: Triangles

Problem 1E

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Question

for a sewing project tanya cut isosceles triangles from a stripes piece pf material where the stripes are parallel the vertex angle of the isosceles triangle is 50 degrees and bx is paralles to the bass

Expert Solution

Step 1

Given: Isosceles triangles are needed to be cut from a stripes piece of material where the stripes are parallel and the vertex angle of the isosceles triangle is 50, and side bx is parallel to the base.

First let's represent this using a picture:

To find the measure of angle bxA.

Step 2

First note that the triangle ABC is isosceles, i.e. AB=AC. And opposite angle of opposite sides are equal, i.e.

$∠ ABC = ∠ ACB$

Also sum of all angles of a triangle is 180ᵒ

$\begin{matrix} ∠ ABC + ∠ ACB + ∠ BAC = 180 ° \\ \Rightarrow 2 ∠ ACB + 50 ° = 180 ° \\ \Rightarrow 2 ∠ ACB = 130 ° \\ \Rightarrow ∠ ACB = 65 ° = ∠ ABC \end{matrix}$

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