(1) The value of x is 25
(2) The measure of ∠CBD is 60°
Explanation:
(1) The given two angles are vertical angles. Since, vertical angles are equal, we can add the two angles to determine the value of x.
Thus, we have,
[tex]5x+15=6x-10[/tex]
Subtracting 5x from both sides, we have
[tex]15=x-10[/tex]
Adding 10 to both sides , we have,
[tex]25=x[/tex]
Thus, the value of x is 25.
(2) It is given that the measure of ∠ABC = (x+7)° and ∠CBD = (2x+14)°
Since, these two angles are supplementary angles and supplementary angles add upto 90°
Thus, we have,
[tex]2x+14+x+7=90[/tex]
Simplifying, we get,
[tex]3x+21=90[/tex]
[tex]3x=69[/tex]
[tex]x=23[/tex]
Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.
[tex]2x+14=2(23)+14=46+14=60[/tex]
Thus, the measure of ∠CBD is 60°
