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 2020-10-26 Answered
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.
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Expert Answer

Benedict
Answered 2020-10-27 Author has 108 answers

Let x be the measure of the first angle.
If the second angle is twice as large as the first, then the second angle must have a measure of 2x.
If the third angle is three-fourths as large as the first, then the third angle must have a measure of 34x
For all triangles, the sum of the three angle measures must equal 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 measures are then:
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 48, 96, and 36, such as the drawing shown below:

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