contestada

Angle Z is 21 degrees larger than twice the measure of angle T. if angle Z and angle T are supplementary,what is the measure of angle T

Respuesta :

Z = 2T + 21
supplementary angles equal 180 degrees
Z + T = 180

2T + 21 + T = 180
3T + 21 = 180
3T = 180 - 21
3T = 159
T = 159/3
T = 53 <====

Z = 2T + 21
Z = 2(53) + 21
Z = 106 + 21
Z = 127

Answer:

[tex]m\angle T=53^{\circ}[/tex]

Step-by-step explanation:

We have been given that angle Z is 21 degree larger than twice the measure of angle T.

[tex]m\angle Z=2m\angle T+21^{\circ}[/tex]

We are also told that angle Z and angle T are supplementary. We can represent this information in an equation as:

[tex]m\angle Z+m\angle T=180^{\circ}[/tex]

[tex]m\angle T+2m\angle T+21^{\circ}=180^{\circ}[/tex]

[tex]3m\angle T+21^{\circ}-21^{\circ}=180^{\circ}-21^{\circ}[/tex]

[tex]3m\angle T=159^{\circ}[/tex]

[tex]\frac{3m\angle T}{3}=\frac{159^{\circ}}{3}[/tex]

[tex]m\angle T=53^{\circ}[/tex]

Therefore, the measure of angle T is 53 degrees.

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