Math Problem Statement
Solution
To solve for in the given figure, we can use the properties of angles and triangles.
Step 1: Analyzing the figure
- We observe that one of the angles in the triangle is a right angle (90°).
- There is a 30° angle at the top and a 40° angle at the bottom right.
Step 2: Using the exterior angle theorem
The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. Here, is an exterior angle, opposite to the 30° and 40° angles.
Thus,
So, the value of is .
Would you like a detailed explanation, or do you have any questions?
Related Questions:
- What is the exterior angle theorem and how is it applied in other scenarios?
- How do different types of triangles (isosceles, equilateral) affect angle properties?
- What are the properties of supplementary and complementary angles?
- How can we solve for unknown angles in polygons with more than three sides?
- How does the sum of interior angles change with the number of sides in a polygon?
Tip:
Remember that in any triangle, the sum of the interior angles is always . This property can help in solving various angle-related problems.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangles
Exterior Angle Theorem
Formulas
Exterior angle = sum of opposite interior angles
Theorems
Exterior Angle Theorem
Triangle Sum Theorem
Suitable Grade Level
Grades 7-10
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