Section 2.5 Formulas and Applications from Geometry 145 Triangles A triangle is one of the basic geometric shapes. It has three sides and the sum of its angles is 180°. A a c b C B a + b + c = 180° We will use this relationship to find the measures of the angles in a triangle. �� ������������������������ ������������������ Find the measure of each angle in the triangle. 6a. A 3a – 15 a + 20 a C B Solution 6a. a + a + 20 + 3a - 15 = 180 Express the relationship. 5a + 5 = 180 Combine like terms. 5a + 5 - 5 = 180 - 5 Subtract 5 from each side. 5a = 175 Simplify. 5a 5 = 175 5 Divide each side by 5. a = 35 Simplify. Since a = 35, the measures of the angles are 35°, 35° + 20° = 55°, and 3(35°) - 15° = 90°. Note that the sum of these measures is 35° + 55° + 90° = 180°. 6b. In a triangle ABC, angles B and C have the same measure. The measure of angle A is four times the measure of either of the other angles. Find the measure of each angle in the triangle. Solution 6b. Draw a diagram to represent the three angles of the triangle. Let a be the measure of angle B. Since angle B and angle C have the same measure, a is also the measure of angle C. Then the measure of angle A is 4a. The sum of the measures of the angles in a triangle is 180°, so we have the following equation. a + a + 4a = 180 Express the relationship. 6a = 180 Combine like terms. 6a 6 = 180 6 Divide each side by 6. a = 30 Simplify. The measure of angles B and C is 30°. The measure of angle A is 4(30) = 120°. Objective 6 ▶ Solve problems involving triangles. A 4a a a C B
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