ABC is a right triangle with the size of angle ACB equal to 74 degrees The lengths of the - Maths - Areas of Parallelograms and Triangles

Question

ABC is a right triangle with the size of angle ACB equal to 74
degrees The lengths of the sides AM, MQ and QP are all equal Find
the measure of angle QPB
​

Shruti Tyagi · Accepted Answer

Dear student,

In rt ∆ABC,∠A+∠B+∠C=180°∠A=180°-74°-90=16°also, In ∆AMQ, As AM=MQ⇒∠AQM=∠MAQ =16°--(equal sides have equal ∠s opp
 to them)∠AQM+∠MAQ +∠AMQ=180°∠AMQ=180°-16-16=148°also, ∠AMQ+∠QMP=180° (linear pair)∠QMP=180°-148°=32°In ∆QMP, QM=QP ⇒ ∠QMP=∠QPM=32°--(equal sides have equal ∠s opp
 to them)∠QPM+∠QPB=180°--(linear pair)∠QPB=180°-32°=148°

Regards

ABC is a right triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB. ​

ABC is a right triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB.