Question

Give that m/_ y=39, find the measures of angles a and b

Answer 1

`\huge\mathbb{ \underline{SOLUTION :}}`

Given:

• 
  `\longrightarrow\bold{m<a= \: 39}` ✓

• 
  `\longrightarrow\bold{m<b= \: 141}`

In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-

`\small\longrightarrow\sf{m<a = m<y}`

`\small\longrightarrow\sf{m<a= \: 39^\circ}`

Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-

`\small\longrightarrow\sf{m<b=m<a+90^\circ}`

`\small\longrightarrow\sf{39^\circ+90^\circ}`

•
`\small\longrightarrow\sf{m<b= 129^\circ}`

`\huge \mathbb{ \underline{ANSWER:}}`

m<a=
`\large\sf{\boxed{\sf 39^\circ}}`

m<b =
`\large\sf{\boxed{\sf 129^\circ}}`

Answer 2

∠a = 39°

∠b = 129°

Explanation:

Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.

Application

Angle y and angle 'a' are vertical angles, so congruent.

∠a = ∠y = 39°

The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.

∠b = ∠a +90° = 39° +90°

∠b = 129°