Question

Find the measure of angle Q

Answer 1

146°

Explanation:

This is an isosceles triangle. By the isosceles triangle theorem, if 2 sides are congruent to one another, then the angles opposite those sides are also congruent to one another. That means that angles P and R are equal. Therefore, we can set them equal to each other, solve for x, plug x back in and solve for the angle value. All triangles, regardless of what type they are, have angles that add up to equal 180. That means that

∠P + ∠Q + ∠R = 180°

Setting P and R equal to each other:

2x + 10 = 6x - 4.

Combining like terms:

14 = 4x so

x = 7/2.

Sub that back into P to find the angle measure of P (and R also, since they are the same):

∠P = 2(7/2) + 10

∠P = 17 so

∠R = 17

If the angles add up to 180, then

∠Q = 180 - 17 - 17 so

∠Q = 146°

Answer 2

The value of ∠Q in the figure is 146⁰.

How to determine the value of The value of ∠Q in the figure.

From the figure

Given

∠P = 2x + 10

∠R = 6x - 4

In ∆PQR

∠P + ∠Q + ∠R = 180⁰(sum of angles in triangle)

Substitute

2x + 10 + ∠Q + 6x - 4 = 180

8x + 6 + ∠Q = 180

But m∠P = m ∠R(base angles of issoceles triangle)

2x + 10 = 6x -4

-4x = -14

x = 7/2

Substitute into 8x + 6 + ∠Q = 180

8(7/2) + 6 + ∠Q = 180

28 + 6 + ∠Q = 180

34 + ∠Q = 180

∠Q = 180 - 34

= 146⁰

The value of ∠Q is 146⁰