Question

If m∠1 = 6x + 2, m∠2 = 16x, find m∠1.

Question 2 options:

A) 67

B) 26

C) 64

D) 27

Answer 1

B) 26

Explanation:

Since the triangle is a right triangle angle 1 and 2 should add to 90 degrees. you would evaluate 6x+2+16x=90. 22x+2=90. 2x=88x. x=4. Plug 4 into the equation for angle 1. 6(4)+2=26

Answer 2

Explanation:

AD is the diameter of the circle. The circle which AB and BC subtends at the circumference of the circle at B is 90 degrees.

The sum of the angles in a triangle i80 degrees. It means that

Angle 1 + angle 2 + 90 = 180 degrees

Angle 1 = 6x + 2

Angle 2 = 16x

Therefore

6x + 2 + 16x + 90 = 180

6x + 16x + 90 + 2 = 180

22x + 92 = 180

Subtracting 92 from both sides of the equation, it becomes

22x + 92 - 92 = 180 - 92

22x = 88

Dividing both sides by 22, it becomes

22x/22 = 88/22

x = 4

Angle 1 = 6x + 2 = 6×4 + 2 = 26 degrees