Question

The figure shows ∠ABD
is 90°, split by line BC. The measure of ∠ABC
is x° and the measure of ∠DBC
is (3x + 10)°. Select all the true statements regarding this figure.

Right angle A B D, split by ray B C, forming adjacent angles A B C and D B C.
x = 20
x = 30

The measure of angle ABC is 20 degrees.


The measure of angle DBC is 60 degrees.


The measure of angle ABC is 30 degrees.


The measure of angle DBC is 70 degrees.

Answer 1

Set up equation: x + (3x + 10) = 90 → 4x + 10 = 90 → 4x = 80 → x = 20.

Then ∠DBC = 3x + 10 = 3(20) + 10 = 70°.

True statements:
- x = 20
- The measure of angle ABC is 20 degrees.
- The measure of angle DBC is 70 degrees.

False statements:
- x = 30
- The measure of angle DBC is 60 degrees.
- The measure of angle ABC is 30 degrees.