Question

Please show work for both problems

Answer 1

(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,

$5x+15=6x-10$

Subtracting 5x from both sides, we have

$15=x-10$

Adding 10 to both sides , we have,

$25=x$

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,

$2x+14+x+7=90$

Simplifying, we get,

$3x+21=90$

       $3x=69$

         $x=23$

Thus, substituting the value of x in ∠CBD = (2x+14)° to determine its value.

$2x+14=2(23)+14=46+14=60$

Thus, the measure of ∠CBD is 60°