# 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.

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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Benedict

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 $\frac{3}{4}x$
For all triangles, the sum of the three angle measures must equal 180.
The sum of the three angles measures of x, 2x, and $\frac{3}{4}x$ is
$x+2x+\frac{3}{4}x=\frac{4x}{4}x+\frac{8x}{4}x+\frac{3}{4}x=\frac{4x+8x+3x}{4}=\frac{15x}{4}$
Since the sum must be equal to 180, then:
$\frac{15x}{4}=180$
$\frac{4}{15}×\frac{15x}{4}=\frac{4}{15}×180$
$x=48$
The three angles measures are then:
First angle: $x={48}^{\circ }$
Second angle: $2x=2\left(48\right)=96$
Third angle: $\frac{3}{4}x=\frac{3}{4}\left(48\right)\right)={36}^{\circ }$
To draw a possible picture, draw a triangle using a protractor and ruler with angle measures of ${48}^{\circ }$, ${96}^{\circ }$, and ${36}^{\circ }$, such as the drawing shown below: