Question

use the figure below for problems 16-17
question 16
1 pts
determine the measurement of ∠cab

Explanation:

Step1: Analyze triangle ABD

In $\triangle ABD$, $\angle D = 90^\circ$, $AD=BD$, so it is an isosceles right triangle. The sum of angles in a triangle is $180^\circ$.
$\angle DAB + \angle DBA + 90^\circ = 180^\circ$, and $\angle DAB = \angle DBA = x-10^\circ$.
So $2(x-10^\circ) + 90^\circ = 180^\circ$

Step2: Solve for x

Simplify the equation:
$2x - 20^\circ + 90^\circ = 180^\circ$
$2x + 70^\circ = 180^\circ$
$2x = 180^\circ - 70^\circ = 110^\circ$
$x = 55^\circ$

Answer:

$55^\circ$