Question

If angle ABD is 90 degrees, select all of the angles that measure 42 degrees.
Thank u :)

Answer 1

Measure of angle 2 and angle 4 is 42°.

Explanation:

m∠ABC = 42°

m(∠ABD) = 90°

m(∠ABD) = m(∠ABC) + m(∠DBC)

90° = 43° + m(∠DBC)

m(∠DBC) = 90 - 43 = 47°

Since ∠ABC ≅ ∠4 [Vertical angles]

m∠ABC = m∠4 = 42°

Since, m∠3 + m∠4 = 90° [Complimentary angles]

m∠3 + 42° = 90°

m∠3 = 90° - 42°

= 48°

Since, ∠5 ≅ ∠3 [Vertical angles]

m∠5 = m∠3 = 48°

m∠3 + m∠2 = 90° [given that m∠2 + m∠3 = 90°]

m∠2 + 48° = 90°

m∠2 = 90 - 48 = 42°

m∠3+ m∠4 = 90° [Since, ∠3 and ∠4 are the complimentary angles]

48° + m∠4 = 90°

m∠4 = 90 - 48 = 42°

Therefore, ∠2 and ∠4 measure 42°.