Question

In triangle abc, the measure of angle a is fifteen less than twice the measure of angle

Answer 1

Answer:

{35}^{\circ}

Step-by-step 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 ${35}^{\circ}$

Answer 2

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