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Math

QuestionFind the value of xx in a triangle where an exterior angle is 144 degrees and one interior angle is 93 degrees.

Studdy Solution

STEP 1

Assumptions1. The triangle is a simple triangle with three interior angles. . The straight line forms a linear pair with one of the interior angles of the triangle.
3. The angle on the straight line outside the triangle is144 degrees.
4. One of the interior angles of the triangle at the bottom corner is93 degrees.
5. The other interior angle of the triangle is xx degrees.

STEP 2

We know that the sum of the angles on a straight line is180 degrees. So, we can find the value of the angle formed by the straight line and the triangle by subtracting the given exterior angle from180 degrees.
Angle on the straight line with the triangle=180 degrees−Exterior angleAngle\, on\, the\, straight\, line\, with\, the\, triangle =180\, degrees - Exterior\, angle

STEP 3

Now, plug in the given value for the exterior angle to calculate the angle on the straight line with the triangle.
Angle on the straight line with the triangle=180 degrees−144 degreesAngle\, on\, the\, straight\, line\, with\, the\, triangle =180\, degrees -144\, degrees

STEP 4

Calculate the angle on the straight line with the triangle.
Angle on the straight line with the triangle=180 degrees−144 degrees=36 degreesAngle\, on\, the\, straight\, line\, with\, the\, triangle =180\, degrees -144\, degrees =36\, degrees

STEP 5

We know that the sum of the interior angles of a triangle is180 degrees. So, we can find the value of xx by subtracting the given interior angle and the calculated angle from180 degrees.
x=180 degrees−Given interior angle−Angle on the straight line with the trianglex =180\, degrees - Given\, interior\, angle - Angle\, on\, the\, straight\, line\, with\, the\, triangle

STEP 6

Now, plug in the given value for the interior angle and the calculated angle on the straight line with the triangle to calculate xx.
x=180 degrees−93 degrees−36 degreesx =180\, degrees -93\, degrees -36\, degrees

STEP 7

Calculate the value of xx.
x=180 degrees−93 degrees−36 degrees=51 degreesx =180\, degrees -93\, degrees -36\, degrees =51\, degreesThe other interior angle of the triangle is51 degrees.

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