Find the missing measures. m∠1 = _____°.
Understand the Problem
The question is asking to find the measure of angle 1 in a triangle using the Exterior Angle Theorem. The given angles are 57° and 6.2°.
Answer
$$ m\angle 1 = 63.2^\circ $$
Answer for screen readers
$$ m\angle 1 = 63.2^\circ $$
Steps to Solve
-
Identify the Exterior Angle Theorem The Exterior Angle Theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.
-
Determine the angles involved Given the angles in the triangle:
- One interior angle is (57^\circ)
- The other interior angle is (6.2^\circ)
-
Apply the theorem In this triangle, the exterior angle (which corresponds to angle 1) can be calculated using the theorem: $$ m\angle 1 = 57^\circ + 6.2^\circ $$
-
Calculate the result Now perform the addition: $$ m\angle 1 = 57 + 6.2 = 63.2^\circ $$
$$ m\angle 1 = 63.2^\circ $$
More Information
The Exterior Angle Theorem is a fundamental theorem in geometry that helps relate the exterior angles of triangles to the interior angles. This problem illustrates how the measures of angles in a triangle can be calculated easily using this theorem.
Tips
- Forgetting to add both interior angles to find the exterior angle.
- Misreading angle measures; ensure the angles are clear before using them in calculations.
AI-generated content may contain errors. Please verify critical information
