Question

select all the true statements given the figure.
a. m∠4 = m∠2
b. m∠4 = m∠1 + m∠2
c. m∠4 = 180 - m∠3
d. m∠4 = m∠1 + m∠2 + m∠3
e. m∠4 = m∠3 + m∠1

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°, so \(m\angle1 + m\angle2+m\angle3 = 180^{\circ}\). Also, \(\angle3\) and \(\angle4\) are a linear - pair.

Step2: Use the linear - pair property

Since \(\angle3\) and \(\angle4\) are a linear - pair, \(m\angle3 + m\angle4=180^{\circ}\). Then \(m\angle4 = 180 - m\angle3\), so statement C is true.

Step3: Use the exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the given triangle, \(\angle4\) is an exterior angle, and the non - adjacent interior angles are \(\angle1\) and \(\angle2\). So \(m\angle4=m\angle1 + m\angle2\), and statement B is true.

Answer:

B. \(m\angle4 = m\angle1 + m\angle2\)
C. \(m\angle4 = 180 - m\angle3\)