contestada

In triangle abc, the measure of angle a is fifteen less than twice the measure of angle
b. the measure of angle c equals the sum of the measures of angle a and angle b, determine the measure of angle b

Respuesta :

sara2oo1
Angle b is 35 because angle a is (2b-15) and angle c is (3b-15) and b is (b) and angles in a triangle add to 180 so (2b-15)+(3b-15)+(b)=180, so (6b-30)=180 / 6b= 210 so b is 35
aachen

Answer:

{35}^{\circ}

Step-by-step explanation:

GIven: In Δ[tex]\text{abc}[/tex], the measure of angle [tex]\angle \text{a}[/tex] is fifteen less than twice the measure of [tex]\angle \text{b}[/tex]. the measure of angle [tex]\angle \text{c}[/tex] equals the sum of the measures of angle [tex]\angle \text{a}[/tex] and angle [tex]\angle \text{b}[/tex].

To Find: determine the measure of angle  [tex]\angle \text{b}[/tex].

Solution:

In Δ[tex]\text{abc}[/tex],

[tex]m\angle \text{a}+m\angle \text{b}+m\angle \text{c}={180}^{\circ}[/tex]

also,

[tex]m\angle\text{a}=2m\angle\text{b}-{15}^{\circ}[/tex]

[tex]m\angle\text{c}=m\angle\text{a}+m\angle\text{b}[/tex]

putting value of [tex]\angle\text{c}[/tex]

[tex]m\angle\text{a}+m\angle\text{b}+m\angle \text{a}+m\angle\text{b}={180}^{\circ}[/tex]

[tex]2(m\angle\text{a}+m\angle\text{b})={180}^{\circ}[/tex]

[tex]m\angle\text{a}+m\angle\text{b}={90}^{\circ}[/tex]

putting value of [tex]\angle\text{a}[/tex]

[tex]2m\angle\text{b}-{15}^{\circ}+m\angle\text{b}={90}^{\circ}[/tex]

[tex]3m\angle\text{b}={90}^{\circ}+{15}^{\circ}[/tex]

[tex]m\angle\text{b}={35}^{\circ}[/tex]

Therefore [tex]\angle\text{b}[/tex] is [tex]{35}^{\circ}[/tex]