Question

Given: mEDF = 120°; mADB = (3x)°; mBDC = (2x)°

Prove: x = 24


What is the missing reason in step 3?



vertical angles are congruent
substitution
definition of congruency
definition of equality

Answer 1

This is the concept of geometry, we are required to find the value of x given that:
1. m<EDF=120 [Given]
m<(ADB)=3x
m<BDC=2x
2.<EDF and <ADC are vert. <s [def of vert angles]
3.<EDF=<ADC [vertical angles are equal]
The reason number 3 is, vertical angles are equal

Answer 2

The correct answer is:

vertical angles are congruent

Step-by-step explanation:

In the proof, we are shown that ∠EDF and ∠ADC are vertical angles. This is because they are opposite each other and share only a vertex.

The vertical angle theorem tells us that vertical angles are congruent; therefore ∠EDF ≅ ∠ADC.