This document contains solutions to 4 geometry problems involving parallelograms, rhombi, and finding angles of polygons. The problems involve setting up and solving equations based on properties of the shapes. The solutions find side lengths, angles, and use sums of interior angles to solve for variables.

1. By: Raluto, Randel Roy G.
Don Carlos Polytechnic College
Student teacher

2. Given: parallelogram ABCD
, sides as marked.
Find AD.
Solution:
6x - 10 = x + 5 (opposite sides)
3x - 10 = 5;
3x = 15; x = 5
AD = 4x - 5 = 4(5) - 5 = 15

3. Given: parallelogram DEFG,
∠s as marked.
Find m∠F,
Solution:∠D supplementary
to ∠E
(2x+12) + (5x) = 180
7x + 12 = 180;
7x = 168;
x = 24
m∠F = 2(24) + 12 = 60º

4. Given: rhombus ABCD with diagonals
drawn.
If AE = 6x + 6 ; CE = 15x – 3
Find CA.
Solution: AE = CE
6x + 6 = 15x - 3
6x - 15x = -3 - 6; 9x = ; x = 1
AE = 6x + 6 = 6(1) + 6 = 12
CE = 15x - 3 = 15(1) - 3 = 12
CE + AE = CA
12 + 12 = 24

5. Given: m∠A = 3x+9
m∠B = 5x+20
m∠C = 3x
m∠D = 2x+6
Find m∠D.
Solution: 3x+9 + 5x+20 + 3x + 2x+6 = 360
13x + 35 = 360;
13x = 325;
x = 25
m∠D = 2(25)+6 = 56º

6. Given: m∠A = 4x+16
m∠B = 2x+20
m∠C = 2x
m∠D = 2x+6
Find m∠D.