University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

150

Pages:

3
Author:

anon

Angle Relationships in Quadrilaterals Sum of Interior Angles ◦ Sum of Exterior Angles ◦ 𝑚 ∠𝐵𝐶𝐷 = 80. 25 𝑚 ∠𝐺𝐶𝐵 = 99. 75 ◦ ◦ 𝑚 ∠𝐶𝐷𝐴 = 67. 10 𝑚 ∠𝐹𝐵𝐴 = 60. 42 ◦ ◦ 𝑚 ∠𝐴𝐵𝐶 = 93. 07 𝑚 ∠𝐸𝐴𝐷 = 87. 54 ◦ ◦ 𝑚 ∠𝐴𝐵𝐶 = 119. 58 𝑚 ∠𝐻𝐷𝐶 = 112. 28 𝑚 ∠𝐵𝐶𝐷 + 𝑚 ∠𝐶𝐷𝐴 + 𝑚 ∠𝐷𝐴𝐵 + 𝑚 ∠𝐵𝐶𝐷 + 𝑚 ∠𝐶𝐷𝐴 + 𝑚 ∠𝐷𝐴𝐵 + 𝑚 The sum of the interior angles in a The sum of the interior angles in quadrilateral is 360◦ ◦ a quadrilateral is 360 Ex. 1: Determine the unknown measures. Justify your calculations. Solution: Find x and y. 1) Find x: ◦ Since x and 85 are supplementary angles, then x+85=180 𝑋 = 180 − 85 ◦ 𝑋 = 95 2) Find y: ◦ The sum of the interior angles in a quadrilateral is 360 ◦ ◦ ◦ So, 70 + 110 + 𝑦 + 𝑥 += 360 ◦ ◦ ◦ ◦ 70 + 110 + 𝑦 + 95 = 360 ◦ ◦ 275 + 𝑦 = 360 𝑦 = 360 − 275 ◦ 𝑦 = 85 ◦ ◦ 𝑥 = 95 , 𝑦 = 85 Ex. 2: Omar calculates that x represents an angle measure of 50°. Is he correct? How do you know? Solution: We know that the sum of the exterior angles in a ◦ quadrilateral is 360 ◦ ◦ ◦ ◦ 𝑋 + 125 + 95 + 90 = 360 ◦ ◦ 𝑋 + 310 = 360 𝑋 = 360 − 310 𝑋 = 50 Ex. 3: Calculate the measure of angle P. Explain your calculation Solution: We know that the sum of the exterior angles in a ◦ quadrilateral is 360 ◦ ◦ ◦ ◦ ∠𝑃 + 90 + 70 + 90 = 360 ◦ ◦ ◦ ◦ ∠𝑃 + 250 = 360 ∠𝑃 = 360 − 250 ◦ ∠𝑃 = 110