USE RHOMBUS ABCD. FIND VALUE OF X, IF M DCB = 5X - 10 AND M DAC = X + 10.
In a rhombus, opposite angles are equal, and the diagonals bisect the angles.
So if angle DAC = x+10
then angle DAB = 2x + 20
then 5x-10 = 2x+20
3x = 30
x = 10
To find the value of x in the rhombus ABCD, we can use the fact that opposite angles in a rhombus are equal.
1. Start by considering angles DCB and DAC. We are given that the measure of angle DCB is 5x - 10 and the measure of angle DAC is x + 10. Since these two angles are opposite angles in the rhombus, they must be equal.
2. Set up an equation to solve for x:
5x - 10 = x + 10
3. Simplify the equation by combining like terms:
5x - x = 10 + 10
4x = 20
4. Solve for x by dividing both sides of the equation by 4:
4x/4 = 20/4
x = 5
Therefore, the value of x is 5.