Question

Let Q be in the interior of RST. find the measure of each angle using the angle addition postulate and explain how you found each angle measure

Answer in a simple way please (:

Answer 1

Using the angle addition postulate, the angle measures are:

$m\angle RSQ = 28^{\circ}\\\\m\angle QST= 33^{\circ}$

(See the image attached below showing the angles given.)

Recall:

The angle addition postulate states that two smaller angles within a bigger angle will add up to give the sum of the larger one.

Given:

$m \angle RST = 3x + 7\\\\m \angle QST = 5x - 2\\\\m \angle RST = 61$

• Thus:

$m\angle RSQ + m\angle QST = m\angle RST$ (angle addition postulate)

• Substitute

$3x + 7 + 5x - 2 = 61$

• Add like terms

$8x + 5 = 61$

• Subtract 5 from each side

$8x + 5 = 61\\\\8x = 61 - 5\\\\8x = 56$

• Divide both sides by 8

$x = 7$

• Find $m \angle RSQ$

$m\angle RSQ = 3x + 7$

• Plug in the value of x

$m\angle RSQ = 3(7) + 7\\\\m\angle RSQ = 28^{\circ}$

• Find $m \angle RSQ$

$m\angle QST= 5x - 2$

• Plug in the value of x

$m\angle QST= 5(7) - 2\\\\m\angle QST= 33^{\circ}$

Therefore, using the angle addition postulate, the angle measures are:

$m\angle RSQ = 28^{\circ}\\\\m\angle QST= 33^{\circ}$

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