Question

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

Answer 1

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

Answer 2

{35}^{\circ}

Explanation:

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

To Find: determine the measure of angle
`\angle \text{b}`.

Solution:

In Δ
`\text{abc}`,

`m\angle \text{a}+m\angle \text{b}+m\angle \text{c}={180}^(\circ)`

also,

`m\angle\text{a}=2m\angle\text{b}-{15}^(\circ)`

`m\angle\text{c}=m\angle\text{a}+m\angle\text{b}`

putting value of
`\angle\text{c}`

`m\angle\text{a}+m\angle\text{b}+m\angle \text{a}+m\angle\text{b}={180}^(\circ)`

`2(m\angle\text{a}+m\angle\text{b})={180}^(\circ)`

`m\angle\text{a}+m\angle\text{b}={90}^(\circ)`

putting value of
`\angle\text{a}`

`2m\angle\text{b}-{15}^(\circ)+m\angle\text{b}={90}^(\circ)`

`3m\angle\text{b}={90}^(\circ)+{15}^(\circ)`

`m\angle\text{b}={35}^(\circ)`

Therefore
`\angle\text{b}` is
`{35}^(\circ)`