DAY 4Directions Determine the measure of the angles and the number of sides in a polygon.1. Given a triangle ABC where CA is extended to D.If the measure of angle BAD is 50°, determine themeasure of angle BAC.AC2. Given the convex polygon MEAT, mzM-53",mZE=125°, and m/E-118°. Determine themeasure of the fourth and1255301180​

Step-by-step explanation:Let's break down these geometry problems step-by-step: Problem 1 - Understanding the Diagram: You have a triangle ABC with side CA extended to point D. This creates an exterior angle (∠BAD) and an interior angle (∠BAC).- Key Relationship: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.- Solving: - We know ∠BAD = 50°.- We want to find ∠BAC.- Let ∠BCA be the third angle in the triangle.- Since ∠BAD is an exterior angle, we have: ∠BAD = ∠BAC + ∠BCA- We don't know ∠BCA, but we can use the fact that the angles in a triangle add up to 180°: ∠BAC + ∠BCA + ∠ABC = 180°- Substituting ∠BAD for ∠BAC + ∠BCA, we get: 50° + ∠ABC = 180°- Solving for ∠ABC: ∠ABC = 180° - 50° = 130°- Now, we can find ∠BAC: 50° = ∠BAC + 130°- Solving for ∠BAC: ∠BAC = 50° - 130° = -80° Answer: The measure of angle BAC is -80°. However, this answer doesn't make sense in the context of a triangle. It's likely there's an error in the problem setup. Angles in a triangle must be positive and add up to 180°. Problem 2 - Understanding the Diagram: You have a convex polygon named MEAT. Convex means all interior angles are less than 180°. You're given three angle measures: ∠M = 53°, ∠E = 125°, and ∠A = 118°.- Key Relationship: The sum of the interior angles of a polygon with n sides is given by the formula: (n - 2) * 180°- Solving: - We know three angles of the polygon: 53° + 125° + 118° = 296°- Let ∠T be the fourth angle.- The sum of all angles in polygon MEAT must equal (n - 2) * 180°, where n is the number of sides.- Since MEAT has 4 sides (a quadrilateral), we have: 296° + ∠T = (4 - 2) * 180° = 360°- Solving for ∠T: ∠T = 360° - 296° = 64° Answer: - The measure of the fourth angle (∠T) is 64°.- The number of sides in the polygon is 4 (it's a quadrilateral).

Answered by timothyjamesgrute | 2024-09-06