Question

1. the measure of one acute angle in a right triangle is 5 times the measure of the other acute angle. what is the measure of the larger acute angle?

larger acute angle measure =

1. what is ( mangle1 )?

( mangle1 = )

Explanation:

Step1: Find the value of \(x\)

According to the exterior - angle theorem of a triangle, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \((7x - 16)=(x + 8)+4x\)

$$
LATEXBLOCK0
$$

Step2: Calculate \(m\angle1\)

We know that \(m\angle1=(7x - 16)-(x + 8)\)
Substitute \(x = 12\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

\(48^{\circ}\)