The second angle in a triangle is twice as large as the first. The third angle is three-fourths as large as the first. Find the angle measures and draw a possible picture.

snowlovelydayM

snowlovelydayM

Answered question

2020-10-26

The second angle in a triangle is twice as large as the first. The third angle is three-fourths as large as the first. Find the angle measures and draw a possible picture.

Answer & Explanation

Benedict

Benedict

Skilled2020-10-27Added 108 answers

Let x represent the initial angle's measurement.
The second angle must have a measure of 2x if it is two times as large as the first. If the third angle is three-fourths as large as the first, then the third angle must have a measure of 34x
The total of the three angle measurements for each triangle must be 180.
The sum of the three angles measures of x, 2x, and 34x is
x+2x+34x=4x4x+8x4x+34x=4x+8x+3x4=15x4
Since the sum must be equal to 180, then:
15x4=180
415×15x4=415×180
x=48
The three angles are as follows:
First angle: x=48
Second angle: 2x=2(48)=96
Third angle: 34x=34(48))=36
To draw a possible picture, draw a triangle using a protractor and ruler with angle measures of 4896, and 36, such as the drawing shown below:

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