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!