Question

Using the picture below, write and solve an equation to find x. Then, find m/ABD and m/DBC (the measures

of the two angles). Assume points A, B, and C are collinear.

Answer 1

Below:

Explanation:

Given, points A, B, and C are collinear,i.e. they all lie on same straight line, ABC.

Since ABC is a straight line, we can apply a theorem known as linear pair theorem, according to which in a line,

• <a + <b = 180°,where<a and<b are angles on it.

According to the question,

<a = 7x-3

<b = 3x+13

• 7x-3+3x+13 = 180°

Solve the equation.

• 10x + 10 = 180
• 10x = 180-10 = 170
• x = 17°

Hence, the value of x stands 17°

Here m<ABD = 7x - 3

Putting the value of x,

• m<ABD = 7*17-3 = 119 - 3 = 116°

Here m<CBD = 3x+13

Putting the value of x,

• m<CBD = 3*17 + 14 = 51+13 = 64°