Question

Find the unknown angles of triangles.
Please help me...!!!​

Answer 1

Let's take this fun problem step-by-step:

Let's first analyze the triangle:  ΔBRE

  ∠B + ∠E + ∠R = 180

  45 + 35 + ∠R = 180

    ∠R = 100   ⇒ ∠BRE = 100 degrees

Now let's analyze ΔAQD

 ∠A + ∠Q + ∠D = 180

 30 + ∠Q + 50 = 180

    ∠Q = 100 degrees ⇒ ∠AQD = 180 degrees

Now let's consider another fact:

• AQC is a straight line

           ⇒ meaning that ∠AQD + ∠RQC = 180 degrees

              ⇒ ∠RQC = 180 degrees - ∠AQD = 180 - 100 = 80 degrees

• CRE is a straight line

            ⇒ meaning that ∠BRE + ∠BRC = 180 degrees

                ⇔ ∠BRC = 180 degrees - ∠BRE = 180 - 100 = 80 degrees

Now let's consider ΔQRC:

  ∠BRC + ∠RQC + ∠QCR = 180 degrees

   80 + 80 + x = 180

         x = 20 degrees

Answer: 20 degrees

Hope that helps!