Question

which statements are always true regarding the diagram? check all that apply.
□ ( mangle3 + mangle4 = 180^circ )
□ ( mangle2 + mangle4 + mangle6 = 180^circ )
□ ( mangle2 + mangle4 = mangle5 )
□ ( mangle1 + mangle2 = 90^circ )
□ ( mangle4 + mangle6 = mangle2 )
□ ( mangle2 + mangle6 = mangle5 )

Explanation:

Step1: Check supplementary angles

∠3 and ∠4 form a straight line, so their sum is 180°. So m∠3 + m∠4 = 180° is true.

Step2: Check triangle angle sum

∠2, ∠4, ∠6 are angles of a triangle. Triangle angles sum to 180°, so m∠2 + m∠4 + m∠6 = 180° is true.

Step3: Check exterior angle theorem

∠5 is an exterior angle of the triangle, equal to sum of remote interior angles ∠2 and ∠4. So m∠2 + m∠4 = m∠5 is true.

Step4: Check other statements

No info shows ∠1 + ∠2 = 90° (not necessarily right angle). ∠4 + ∠6 ≠ ∠2 (they sum to 180°−∠2). ∠2 + ∠6 ≠ ∠5 (∠5 = ∠2 + ∠4). So these are false.

Answer:

m∠3 + m∠4 = 180°, m∠2 + m∠4 + m∠6 = 180°, m∠2 + m∠4 = m∠5