Question

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

Answer 1

Answer:

  ∠a = 39°

  ∠b = 129°

Step-by-step 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°

Answer 2

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

Given:

• $\longrightarrow\bold{m$ ✓

• $\longrightarrow\bold{m$

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

$\small\longrightarrow\sf{m$

$\small\longrightarrow\sf{m$

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

$\small\longrightarrow\sf{m$

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

• $\small\longrightarrow\sf{m$

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

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

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