Question

Find the measure of each angle

m∠A =

m∠B =

m∠BCA =

Answer 1

Finding the bottom left angle of the triangle:

Before we solve for each angle, let's find the bottom left angle of the triangle.

We know that:

• Straight line = 106 + x
• Straight line = 180

This means that:

• ⇒ 106 + x = 180

Step-by step calculations:

⇒ 106 + x = 180

⇒ 106 - 106 + x = 180 - 106

⇒ x = ∠BCA = 74°

Solving for y:

We know that:

⇒ Sum of the interior angles of the triangle: 180°

This means that:

⇒ (74) + (3y + 22) + (4y) = 180

Step-by step calculations:

⇒ (74) + (3y + 22) + (4y) = 180

⇒ 96 + 7y = 180

⇒ 96 - 96 + 7y = 180 - 96

⇒ 7y = 84

⇒ 7y/7 = 84/7

⇒ y = 12

Finding the measure of each angle:

Step-by step calculations:

⇒ ∠B = 3y + 22

⇒ ∠B = 3(12) + 22

⇒ ∠B = 36 + 22

⇒ ∠B = 58°

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⇒ ∠A = 4y

⇒ ∠A = 4(12)

⇒ ∠A = 48°