Question

Rays DA and DC are perpendicular. Point B lies in the interior of angle ADC. If m angle ADB=(3a+10)degrees and m angle BDC=13adegrees, find a, m angle ABD, and m angle DBC.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

∠ ADB = 3a + 10

∠ BDC = 13a

DA and DC are perpendicular

Step 02

Graph

Step 03:

(3a + 10) + 13a = 90

16a + 10 = 90

16a = 90 - 10

a = 80 / 16

a = 5

m ∠ ADB = 3a + 10 = 3*5 + 10 = 15 + 10 = 25°

m ∠ BDC = 13a = 13 * 5 = 65°

The solution is:

a = 5

m ∠ ADB = 25°

m ∠ BDC = 65°