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EastWind [94]
3 years ago
6

In angle ABC, ray BX is in the interior of the angle, the measure of angle ABX is 12 more than 4 times the measure of angle CBX,

and the measure of angle ABC = 92 degrees.
a. Draw a diagram to represent the situation.
b. Write and solve an equation to find the measure of angle ABX and the measure of angle CBX.

Any help is much appreciated! :)
Mathematics
1 answer:
Alex73 [517]3 years ago
6 0
To start you should represent CBX as x. so, an equation would be                       92 = x + 4x + 12. This is the equation so, 92 is the total angle, and the 12x + 4 is the ABX part. So, once you solve the problem you should get CBX=76 and ABX=16
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12. Find the measure of each interior angle of triangle QRT.
Veseljchak [2.6K]

Answer:

\angle QRT=125.6\°

\angle RTQ=6.4\°

\angle TQR=48\°

Step-by-step explanation:

It is important to remember that, by definition, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

In this case we can idenfity that the angle 17x is an exterior angle of the triangle QRT. Then:

17x=\angle RTQ+\angle TQR

Where:

\angle RTQ=2x\\\\\angle TQR=48\°

Substituting values and solving for "x", we get:

17x=2x+48\\\\17x-2x=48\\\\15x=48\\\\x=3.2

Then:

17x=17(3.2)=54.4\°\\\\\\\angle RTQ=2(3.2)=6.4\°

The sum of the interior angles of a triangle is 180°, therefore:

\angle QRT+\angle RTQ+\angle TQR=180

Solving for \angle QRT, we get:

\angle QRT=180-48-6.4=125.6\°

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How many exterior angles can be drawn at one vertex of a triangle?
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In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as
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